# Medžuslovjansky matematičny kanon · Open Logic · OLP-0198 To jest polny aktualny kanon terminov, ktory jest použit v medžuslovjanskom izdanje Open Logic. Latinična forma jest redakcijno kanonična; kirilične formy sųt deterministično izvedene. Každy zapis pokazuje smysl, gramatiku, sravnitělne slovjanske formy, dokazy, alternativy, uvěrjenost i revizijnu liniju. English: This is the complete current terminology canon used by the Open Logic Interslavic edition. Latin is the editable canonical witness; Cyrillic is deterministic. Every entry exposes its sense, grammar, Slavic comparanda, evidence, alternatives, confidence and revision lineage. **Kontrolny punkt / checkpoint:** OLP-0198 · 400 aktivnyh zapisov · 453 fizične revizije · OLISV-T0346–OLISV-T0400 dodane od prethodnogo javnogo kontrolnogo punkta. [Ekspertna knjiga odluka / expert decision log](EXPERT_REVIEW_LOG_OLP0198.md) · [machine JSONL](EXPERT_REVIEW_LOG_OLP0198.jsonl) ## OLISV-T0237 · algebra.abelian-group - **English lemma / sense:** abelian group — A group whose binary operation is commutative, named here as an example of a many-sorted object domain. - **Medžuslovjansky:** `Abelova grupa`; lemma `Abelova grupa`; feminine proper-name possessive phrase. - **Upotrěbljenje / inflection:** Genitive Abelovoj grupy; plural Abelove grupy. Preserve Abel as the eponym in citations. - **Kirilična forma:** `Абелова група` - **Argumentacija / rationale:** The direct mathematical group head combines with the officially described -ov possessive pattern for a one-word masculine eponym. - **Uvěrjenost / status:** 0.86 (high); `provisional`; revision `OLISV-T0237-r0001`. - **Slovjanske sravnenja / comparanda:** ru: абелева группа; uk: абелева група; pl: grupa abelowa; cs: Abelova grupa; bcs: Abelova grupa; Абелова група; bg: Абелева група. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[8040]; dictionary_id=1787; lemma=grupa; gloss=group); ISV-GRAMMAR-ADJ (lines 43-45; SHA-256 184348005ACB532868DAEB35DBFB7A8E05A493D550B4D6FA2E1A3BCFC906D84F); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** komutativna grupa: A valid semantic synonym, but it replaces the source's eponym rather than translating it.; abeleva grupa: Less consistent with the established project and official -ov possessive pattern. - **Neizvěstnost / uncertainty:** The complete eponymic phrase is editorially composed; capitalization and national adjective vowels vary. ## OLISV-T0392 · algebra.cancellation-law-addition - **English lemma / sense:** cancellation law for addition — The implication x+y=x+z entails y=z in Peano arithmetic. - **Medžuslovjansky:** `zakon skraćenja dodavanja`; lemma `zakon skraćenja dodavanja`; masculine noun with two genitive complements. - **Upotrěbljenje / inflection:** Zakon is masculine; skraćenja and dodavanja are genitive singular verbal nouns. The shorter contextual form zakon skraćenja is allowed when addition is explicit. - **Kirilična forma:** `закон скрачења додавања` - **Argumentacija / rationale:** Zakon skraćenja is transparent across East, West, and South Slavic algebraic traditions; the explicit dodavanja complement preserves canon T0366's distinction between the operation and its result suma. - **Uvěrjenost / status:** 0.79 (medium); `provisional`; revision `OLISV-T0392-r0001`. - **Slovjanske sravnenja / comparanda:** ru: закон сокращения сложения; uk: закон скорочення додавання; pl: prawo skracania dodawania; cs: zákon krácení sčítání; bcs: zakon skraćivanja zbrajanja; закон скраћивања сабирања; bg: закон за съкращаване при събиране. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[10042]; dictionary_id=1901; lemma=zakon; gloss=law); ISV-DICT-LIVE-20260825 (wordList[15357]; dictionary_id=3139; lemma=skraćati; gloss=shorten, abbreviate); ISV-DICT-LIVE-20260825 (wordList[287]; dictionary_id=1704; lemma=dodavati; gloss=add); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic and standard flavorization) - **Alternativy / alternatives:** zakon poniščenja dodavanja: Poniščenje suggests inversion or annulment rather than cancelling a common addend from an equality.; zakon skraćenja sumy: Suma is the arithmetic result in canon T0387; the law concerns the addition operation, not shortening one result object. - **Neizvěstnost / uncertainty:** The dictionary skraćati row is nontechnical; the algebraic sense is an evidence-linked editorial extension. ## OLISV-T0389 · algebra.commutativity-of-addition - **English lemma / sense:** commutativity of addition — The property that interpreted addition has the same value after its two arguments are exchanged; the unit shows that Robinson Q does not prove it. - **Medžuslovjansky:** `komutativnost dodavanja`; lemma `komutativnost dodavanja`; feminine abstract noun with genitive complement. - **Upotrěbljenje / inflection:** Use komutativnost dodavanja for the property. In predicate syntax use dodavanje jest komutativno. The genitive dodavanja follows the operation head OLISV-T0366. - **Kirilična forma:** `комутативност додавања` - **Argumentacija / rationale:** Komutativnost is already established in an accepted Interslavic algebra unit and aligns with direct Russian and Czech specialist evidence. The complement dodavanja deliberately follows current canon OLISV-T0366 rather than the older reader alias sčitanje. - **Uvěrjenost / status:** 0.92 (high); `provisional`; revision `OLISV-T0389-r0001`. - **Slovjanske sravnenja / comparanda:** ru: коммутативность сложения; uk: комутативність додавання; pl: przemienność dodawania; cs: komutativita sčítání; bcs: komutativnost zbrajanja; комутативност сабирања; bg: комутативност на събирането. - **Dokazy / evidence:** OL-MODEL-ARITHMETIC-MODELS-Q (lines 16-21, 113-118, and 172-173); OL-ARITHMETIZATION-CHECKING-DETAILS-ISV (lines 21-30 and 97-101); RU-MI-RAS-PROVABILITY-ARITHMETIC-2020 (physical page 2 / extracted lines 50-56); CS-CUNI-LOGIC-II-2008 (physical page 1 / extracted lines 23-28); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic, standard flavorization) - **Alternativy / alternatives:** komutativnost sčitanja: The property head is sound, but sčitanje is only a retained reader alias; current canon selects dodavanje for the operation.; zaměnimost dodavanja: This calque can suggest general substitutability rather than the exact two-argument exchange law. - **Neizvěstnost / uncertainty:** Polish commonly favors a native property head, while East, West, and South traditions vary in their noun for addition; the edition keeps both the divergence and its current canon choice explicit. ## OLISV-T0186 · algebra.group - **English lemma / sense:** group — A structure with an associative binary operation, an identity element, and inverses, here presented through a first-order axiom system. - **Medžuslovjansky:** `grupa`; lemma `grupa`; feminine noun. - **Upotrěbljenje / inflection:** Feminine noun; genitive grupy, plural grupy. In this formal context it names the algebraic structure, not an informal collection. - **Kirilična forma:** `група` - **Argumentacija / rationale:** Grupa is the exact frozen lemma and is transparent across all six comparison traditions; the current source fixes its algebraic rather than social sense. - **Uvěrjenost / status:** 0.98 (high); `provisional`; revision `OLISV-T0186-r0001`. - **Slovjanske sravnenja / comparanda:** ru: группа; uk: група; pl: grupa; cs: grupa (mat.); bcs: grupa; група; bg: група. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[8040]; dictionary_id=1787; lemma=grupa; gloss=group); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** skupina: The native alternative is common in Czech and some South-Slavic contexts, but it is less uniform across the six traditions and the dictionary explicitly supplies grupa for mathematics. - **Neizvěstnost / uncertainty:** The source gives a right-sided presentation of identity and inverse; the term remains the ordinary group concept under the displayed associativity axiom. ## OLISV-T0246 · algebra.homomorphism - **English lemma / sense:** homomorphism — A structure-preserving map between algebraic or relational structures. - **Medžuslovjansky:** `homomorfizm`; lemma `homomorfizm`; masculine noun. - **Upotrěbljenje / inflection:** Genitive homomorfizma; use homomorfizmom after jest and homomorfizmy in the plural. - **Kirilična forma:** `хомоморфизм` - **Argumentacija / rationale:** The international Greek-derived form is unambiguous in algebra and is the natural name for the source's structure-preserving map. The record does not infer additional algebraic operations beyond the source's statement. - **Uvěrjenost / status:** 0.82 (high); `provisional`; revision `OLISV-T0246-r0002`. - **Slovjanske sravnenja / comparanda:** ru: гомоморфизм; uk: гомоморфізм; pl: homomorfizm; cs: homomorfismus; bcs: homomorfizam; хомоморфизам; bg: хомоморфизъм. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (dictionary_id=16363; lemma=struktura; gloss=structure); ISV-DICT-LIVE-20260825 (dictionary_id=1485; lemma=tělo; gloss=body); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** sȯhranitelj struktury: Descriptive but not the established mathematical noun.; izomorfizm: Too strong: the source has not yet established bijectivity plus inverse preservation. - **Neizvěstnost / uncertainty:** No direct frozen homomorphism row was found in the bounded dictionary; national inflection varies.; The r0001 record remains preserved as adverse provenance for the target/source locator mismatch. ## OLISV-T0252 · algebra.ordered-field - **English lemma / sense:** ordered field — A field equipped with an order compatible with its addition and multiplication. - **Medžuslovjansky:** `uporędženo tělo`; lemma `uporędženo tělo`; neuter adjective-noun phrase. - **Upotrěbljenje / inflection:** Genitive uporędženogo těla; use polno uporędženo tělo for the complete ordered-field phrase. - **Kirilična forma:** `упореджено тєло` - **Argumentacija / rationale:** Tělo is the established Interslavic algebraic carrier for field, while the ordering component follows the pinned oporędčeny family. The source's phrase is reproduced as a descriptive example, not a full axiomatization. - **Uvěrjenost / status:** 0.7 (medium); `provisional`; revision `OLISV-T0252-r0002`. - **Slovjanske sravnenja / comparanda:** ru: упорядоченное поле; uk: впорядковане поле; pl: ciało uporządkowane; cs: uspořádané těleso; bcs: uređeno polje; уређено поље; bg: наредено поле. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (dictionary_id=20002; lemma=oporędčeny; gloss=well-ordered); ISV-DICT-LIVE-20260825 (dictionary_id=1485; lemma=tělo; gloss=body); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** uporędženo polje: Polje is a field component in several languages but is already used for field as a generic area and is less stable in the inherited canon.; linearna algebraična struktura: Too broad and omits the field axioms. - **Neizvěstnost / uncertainty:** The complete phrase is editorial and the source does not list compatibility axioms; no stronger mathematical claim is made.; The r0001 record remains preserved as adverse provenance for the target/source locator mismatch. ## OLISV-T0366 · arithmetic.addition - **English lemma / sense:** addition — The binary arithmetic operation interpreting + in the standard natural-number model and, by transported exponent addition, in the isomorphic one-letter-string model. - **Medžuslovjansky:** `dodavanje`; lemma `dodavanje`; neuter verbal noun. - **Upotrěbljenje / inflection:** Use dodavanje for the operation; genitive dodavanja. At the first reader-facing occurrence retain sčitanje only as a Czech-facing explanatory gloss, not as a second canon head or unrestricted synonym. - **Kirilična forma:** `додавање` - **Argumentacija / rationale:** Dodavanje is a regular, transparent nominalization of the official Interslavic verb dodavati and is directly reinforced by Ukrainian mathematical usage. Because national arithmetic terminology diverges sharply, the first occurrence also gives sčitanje as a narrowly labelled Czech-facing gloss, without promoting the count/census family to a competing canon head. - **Uvěrjenost / status:** 0.9 (high); `provisional`; revision `OLISV-T0366-r0001`. - **Slovjanske sravnenja / comparanda:** ru: сложение; uk: додавання; pl: dodawanie; cs: sčítání; bcs: zbrajanje; bg: събиране. - **Dokazy / evidence:** OL-MODEL-ARITHMETIC-INTRODUCTION (lines 12-22 and 29-34); ISV-DICT-LIVE-20260825 (wordList[287]; dictionary_id=1704; lemma=dodavati; gloss=add); UK-VSPU-MATHEMATICAL-LOGIC-2007 (physical page 64 / extracted lines 2864-2874); CS-CUNI-LOGIC-II-2008 (physical page 1 / extracted lines 25-27); HR-ZAGREB-CLASSICAL-LOGIC-2013 (physical page 66 / extracted line 47); BG-SOFIA-PROLOG-ARITHMETIC-EXERCISE-4 (UTF-8 derivative line 60); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic, standard flavorization) - **Alternativy / alternatives:** sčitanje: Useful as a Czech-facing local gloss, but as a canon head or unrestricted synonym it privileges the West-Slavic count/add family and collides with the direct Interslavic count/census sense.; složenje: It closely follows Russian сложение but risks the broader senses composition or putting together and lacks the direct official Interslavic add verb. - **Neizvěstnost / uncertainty:** The exact noun dodavanje is derived from a directly listed verb rather than independently listed as a specialist dictionary head.; The parenthetical sčitanje is only a Czech-facing explanatory gloss; it is not a canon alias because the same Interslavic family also denotes counting and census. ## OLISV-T0188 · arithmetic.induction-schema - **English lemma / sense:** induction schema — The infinite family of induction instances in first-order arithmetic, one for each permitted formula rather than one second-order axiom. - **Medžuslovjansky:** `shema indukcije`; lemma `shema indukcije`; feminine noun phrase. - **Upotrěbljenje / inflection:** Feminine head with genitive complement; genitive shemy indukcije. Use instance of the schema for one permitted formula. - **Kirilična forma:** `схема индукције` - **Argumentacija / rationale:** The phrase follows a near-unanimous international family and distinguishes an axiom schema from one axiom and from the earlier proof method structural induction. - **Uvěrjenost / status:** 0.94 (high); `provisional`; revision `OLISV-T0188-r0001`. - **Slovjanske sravnenja / comparanda:** ru: схема индукции; uk: схема індукції; pl: schemat indukcji; cs: schéma indukce; bcs: shema indukcije; шема индукције; bg: схема на индукцията. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[14890]; dictionary_id=18814; lemma=shema; gloss=scheme); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** indukcijska shema: The adjectival order is grammatical, but the genitive phrase aligns more uniformly with Russian, Ukrainian, Polish, Czech, Slovak, and the accepted edition's induction terminology. - **Neizvěstnost / uncertainty:** The source itself warns that its displayed schema is simplified; parameters and side conditions are not fully stated. ## OLISV-T0393 · arithmetic.integer-average - **English lemma / sense:** average (integer midpoint) — An element z with x+y=2z or x+y=2z+1; it lies between x and y and is the lower integer midpoint in the remainder-one case. - **Medžuslovjansky:** `srědnje`; lemma `srědnje`; neuter noun. - **Upotrěbljenje / inflection:** Use invariant quoted head srědnje in the defining sentence; the quotation marks signal that the remainder-one case is an integer midpoint, not an exact field mean. - **Kirilična forma:** `срєдње` - **Argumentacija / rationale:** Srědnje is the official dictionary's exact mathematical noun. Quotation marks and the adjacent equations retain the source's useful but slightly loose average label without falsely claiming exact division in the odd case. - **Uvěrjenost / status:** 0.94 (high); `provisional`; revision `OLISV-T0393-r0001`. - **Slovjanske sravnenja / comparanda:** ru: среднее; uk: середнє число; pl: średnia; cs: průměr; střed; bcs: prosjek; просек; bg: средно число. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[1473]; dictionary_id=12566; lemma=srědnje; gloss=average); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic and standard flavorization) - **Alternativy / alternatives:** srědnja vrědnost: The longer calque is unnecessary because the official dictionary directly supplies the neuter mathematical noun srědnje.; polusuma: Half-sum suggests exact division and is false in the remainder-one case unless a floor convention is added. - **Neizvěstnost / uncertainty:** The source calls the lower integer midpoint an average; quotation marks preserve that looseness rather than hiding it. ## OLISV-T0376 · arithmetic.language - **English lemma / sense:** language of arithmetic — The formal first-order language L_A whose nonlogical vocabulary is used to formulate arithmetic structures and theories such as Q. - **Medžuslovjansky:** `jezyk aritmetiky`; lemma `jezyk aritmetiky`; masculine noun phrase with feminine genitive-singular complement. - **Upotrěbljenje / inflection:** Genitive jezyka aritmetiky; locative v jezyku aritmetiky. Use L_A when the source names the formal signature. - **Kirilična forma:** `језык аритметикы` - **Argumentacija / rationale:** Jezyk aritmetiky is the regular genitive compound already patterned by jezyk logiky prvogo reda (OLISV-T0096). Its components are official dictionary heads, while Russian, Czech, and Croatian sources independently attest the specialist construction. - **Uvěrjenost / status:** 0.96 (high); `provisional`; revision `OLISV-T0376-r0001`. - **Slovjanske sravnenja / comparanda:** ru: язык арифметики; uk: мова арифметики; pl: język arytmetyki; cs: jazyk aritmetiky; bcs: jezik aritmetike; језик аритметике; bg: език на аритметиката. - **Dokazy / evidence:** OL-MODEL-ARITHMETIC-STANDARD-MODELS (lines 12-20 and 43-45); ISV-DICT-LIVE-20260825 (wordList[9987]; dictionary_id=541; lemma=język; gloss=language); ISV-DICT-LIVE-20260825 (wordList[1093]; dictionary_id=21256; lemma=aritmetika; gloss=arithmetics); RU-MSU-GODEL-LECTURES-2020 (extracted lines 509-511); CS-CUNI-LOGIC-II-2008 (physical page 1 / extracted lines 23-30); HR-ZAGREB-GODEL-INCOMPLETENESS-2011 (printed page 4 / physical page 6 / extracted lines 172-178); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic, standard flavorization) - **Alternativy / alternatives:** aritmetičny jezyk: The adjectival form is understandable but less directly aligned with the strongest Russian, Czech, and Croatian genitive compounds.; jezyk L_A: L_A is a notation for this particular signature, not the lexical head needed for the dictionary and prose. - **Neizvěstnost / uncertainty:** The compound is a project-house specialist head assembled from official components; no Interslavic standards body has certified it. ## OLISV-T0367 · arithmetic.multiplication - **English lemma / sense:** multiplication — The binary arithmetic operation interpreting the multiplication sign on natural numbers and exponent multiplication in the isomorphic one-letter-string model. - **Medžuslovjansky:** `množenje`; lemma `množenje`; neuter verbal noun. - **Upotrěbljenje / inflection:** Use množenje for the operation; genitive množenja. Keep množit as the corresponding infinitive when verbal syntax is needed. - **Kirilična forma:** `множење` - **Argumentacija / rationale:** Množenje is a transparent action noun from the official Interslavic množiti and coincides exactly with direct Croatian mathematical usage and Ukrainian stem structure. It avoids unnecessary international morphology while remaining recognizable beside Russian and Bulgarian prefixed forms and West-Slavic national terms. - **Uvěrjenost / status:** 0.94 (high); `provisional`; revision `OLISV-T0367-r0001`. - **Slovjanske sravnenja / comparanda:** ru: умножение; uk: множення; pl: mnożenie; cs: násobení; bcs: množenje; bg: умножение. - **Dokazy / evidence:** OL-MODEL-ARITHMETIC-INTRODUCTION (lines 12-22 and 29-34); ISV-DICT-LIVE-20260825 (wordList[11437]; dictionary_id=19858; lemma=množiti; gloss=multiply); RU-MSU-GODEL-LECTURES-2020 (physical page 1 / extracted line 39); UK-VSPU-MATHEMATICAL-LOGIC-2007 (physical page 64 / extracted lines 2864-2874); HR-ZAGREB-CLASSICAL-LOGIC-2013 (physical page 66 / extracted line 47); BG-SOFIA-PROLOG-ARITHMETIC-EXERCISE-4 (UTF-8 derivative line 63); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic, standard flavorization) - **Alternativy / alternatives:** umnoženje: The prefixed form follows Russian and Bulgarian closely but is less neutral across West and South Slavic than the unprefixed official Interslavic base.; multiplikacija: The international loan is intelligible to specialists but is less transparent to readers who recognize the widespread native množ family. - **Neizvěstnost / uncertainty:** The preferred noun is a regular editorial derivation from a directly listed verb rather than a separate dictionary headword. ## OLISV-T0382 · arithmetic.nonstandard-number-in-structure - **English lemma / sense:** non-standard number of an arithmetic structure — An element of an arithmetic-language structure unequal to the value of every standard numeral; the term foregrounds its numerical role while non-standard element foregrounds structure membership. - **Medžuslovjansky:** `nestandardno čislo`; lemma `nestandardno čislo`; neuter adjective-noun phrase. - **Upotrěbljenje / inflection:** Neuter singular nestandardno čislo; instrumental plural nestandardnymi čislami. Use nestandardny element when the source foregrounds membership rather than numerical role. - **Kirilična forma:** `нестандардно число` - **Argumentacija / rationale:** Nestandardno čislo closely follows the direct Croatian phrase and the official adjective and number heads. A separate entry is justified because Open Logic deliberately alternates number and element according to whether the numerical or structural role is foregrounded. - **Uvěrjenost / status:** 0.96 (high); `provisional`; revision `OLISV-T0382-r0001`. - **Slovjanske sravnenja / comparanda:** ru: нестандартное число; uk: нестандартне число; pl: liczba niestandardowa; cs: nestandardní číslo; bcs: nestandardni broj; bg: нестандартно число. - **Dokazy / evidence:** OL-MODEL-ARITHMETIC-NONSTANDARD-MODELS (lines 19-46 and 90-97); ISV-DICT-LIVE-20260825 (wordList[11792]; dictionary_id=37954; lemma=nestandardny; gloss=nonstandard); ISV-DICT-LIVE-20260825 (wordList[11893]; dictionary_id=17215; lemma=čislo; gloss=number); HR-ZAGREB-CLASSICAL-LOGIC-2013 (physical page 66 / extracted lines 69-72); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic, standard flavorization) - **Alternativy / alternatives:** nestandardny element: Correct for the same object when membership is foregrounded, but less faithful where the source explicitly calls it a number.; bezkonečno čislo: Suggests magnitude alone and fails for the general structure-relative definition, which is stated through numeral values. - **Neizvěstnost / uncertainty:** Some national sources prefer non-standard element or describe the non-standard part rather than using a standalone number phrase. ## OLISV-T0187 · arithmetic.peano - **English lemma / sense:** Peano arithmetic — The first-order arithmetic theory using zero, successor, addition, multiplication, order, and an induction schema. - **Medžuslovjansky:** `Peanova aritmetika`; lemma `Peanova aritmetika`; feminine proper-name noun phrase. - **Upotrěbljenje / inflection:** The possessive adjective agrees with aritmetika: genitive Peanovoj aritmetiky. Preserve the mathematician's surname as Peano in citations. - **Kirilična forma:** `Пеанова аритметика` - **Argumentacija / rationale:** The direct international head is unanimous, and Peanova supplies a compact possessive surface familiar to West and South Slavic readers while the comparison table preserves East-Slavic genitive phrasing. - **Uvěrjenost / status:** 0.91 (high); `provisional`; revision `OLISV-T0187-r0001`. - **Slovjanske sravnenja / comparanda:** ru: арифметика Пеано; uk: арифметика Пеано; pl: arytmetyka Peana; cs: Peanova aritmetika; bcs: Peanova aritmetika; Пеанова аритметика; bg: аритметика на Пеано. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[1093]; dictionary_id=21256; lemma=aritmetika; gloss=arithmetics); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** aritmetika Peano: The indeclinable surname phrase is transparent and strong in East Slavic, but the possessive adjective integrates more naturally into the selected Interslavic syntax. - **Neizvěstnost / uncertainty:** The source deliberately gives a simplified induction schema and does not state every parameter or side condition of a full presentation. ## OLISV-T0277 · arithmetic.power - **English lemma / sense:** power — The exponent or degree to which a number is raised in an expression a to the b. - **Medžuslovjansky:** `stųpėnj`; lemma `stųpėnj`; masculine noun. - **Upotrěbljenje / inflection:** Masculine stųpėnj; genitive stųpnja. In the source construction use na ... stųpėnj after vozvesti. - **Kirilična forma:** `ступењ` - **Argumentacija / rationale:** Stųpėnj is the exact pinned dictionary head for degree and is used in the target's raise-to-a-power construction; the displayed exponentials fix the specialist exponent sense. - **Uvěrjenost / status:** 0.9 (high); `provisional`; revision `OLISV-T0277-r0001`. - **Slovjanske sravnenja / comparanda:** ru: степень; uk: степінь; pl: potęga; cs: mocnina; bcs: stepen; степен; bg: степен. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 37-58); ISV-DICT-LIVE-20260825 (dictionary_id=3252; lemma=stųpėnj; gloss=degree, stair); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** potencija: The international form is less broadly stable and can denote potency or exponentiation rather than the exponent itself. - **Neizvěstnost / uncertainty:** The dictionary gloss says degree rather than exponent; the mathematical specialization is fixed by the source and target syntax. ## OLISV-T0388 · arithmetic.product-result - **English lemma / sense:** product — The result of applying the interpreted multiplication operation to two elements, distinguished from the operation of multiplication itself. - **Medžuslovjansky:** `proizvod`; lemma `proizvod`; masculine noun. - **Upotrěbljenje / inflection:** Masculine singular proizvod; genitive proizvoda. Use množenje for the operation and proizvod for the resulting value. - **Kirilična forma:** `производ` - **Argumentacija / rationale:** The dictionary marks proizvod specifically as mathematical product, while produkt is its generic product head. Proizvod therefore preserves the specialist result sense and remains distinct from canon head množenje for the operation. - **Uvěrjenost / status:** 0.96 (high); `provisional`; revision `OLISV-T0388-r0001`. - **Slovjanske sravnenja / comparanda:** ru: произведение; uk: добуток; pl: iloczyn; cs: součin; bcs: proizvod; производ; bg: произведение. - **Dokazy / evidence:** OL-MODEL-ARITHMETIC-MODELS-Q (lines 52-60); ISV-DICT-LIVE-20260825 (wordList[13493]; dictionary_id=22261; lemma=proizvod; gloss=product (math.)); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic, standard flavorization) - **Alternativy / alternatives:** produkt: The dictionary reserves a separate proizvod row specifically for the mathematical sense; produkt is broader and already serves other canon compounds.; množenje: Already canonized as the operation or process, not the resulting value. - **Neizvěstnost / uncertainty:** West- and East-Slavic national traditions use unrelated native result nouns; the official Interslavic math-specific row resolves the edition choice. ## OLISV-T0377 · arithmetic.robinson-q - **English lemma / sense:** Robinson arithmetic Q — The finitely axiomatized weak arithmetic theory Q used here to ensure numeral separation and the basic arithmetic facts needed for the standard-model isomorphism proof; unlike PA, it has no induction schema. - **Medžuslovjansky:** `Robinsonova aritmetika`; lemma `Robinsonova aritmetika`; feminine possessive-adjective noun phrase. - **Upotrěbljenje / inflection:** Feminine nominative Robinsonova aritmetika; genitive Robinsonovoj aritmetiky. Append the protected theory symbol Q in prose when the specific formal theory must be distinguished. - **Kirilična forma:** `Робинсонова аритметика` - **Argumentacija / rationale:** Robinsonova aritmetika Q follows a transparent Slavic possessive-adjective construction and exactly matches the direct Croatian specialist term; Russian and Czech independently identify the same theory and its missing induction schema. The Q suffix is retained because it distinguishes the formal theory from arithmetic as a subject. - **Uvěrjenost / status:** 0.95 (high); `provisional`; revision `OLISV-T0377-r0001`. - **Slovjanske sravnenja / comparanda:** ru: арифметика Робинсона Q; uk: арифметика Робінсона Q; pl: arytmetyka Robinsona Q; cs: Robinsonova aritmetika Q; bcs: Robinsonova aritmetika Q; Робинсонова аритметика Q; bg: аритметика на Робинсън Q. - **Dokazy / evidence:** OL-MODEL-ARITHMETIC-STANDARD-MODELS (lines 59-113); ISV-DICT-LIVE-20260825 (wordList[1093]; dictionary_id=21256; lemma=aritmetika); RU-MI-RAS-PROVABILITY-ARITHMETIC-2020 (physical page 2 / extracted lines 39-52); CS-CUNI-LOGIC-II-2008 (physical page 1 / extracted lines 23-30); HR-ZAGREB-GODEL-INCOMPLETENESS-2011 (printed pages 4-5 / physical pages 6-7 / extracted lines 196-212); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic, standard flavorization) - **Alternativy / alternatives:** aritmetika Robinsona: The genitive-name construction is strongly supported in Russian and Polish-style usage, but the possessive adjective is more compact and directly attested in Croatian and Czech.; teorija Q: Useful after introduction, but too opaque as the dictionary head and it suppresses the established eponym. - **Neizvěstnost / uncertainty:** The full phrase is a provisional edition term; no direct Ukrainian or Bulgarian specialist occurrence is pinned in this packet. ## OLISV-T0381 · arithmetic.standard-number-in-structure - **English lemma / sense:** standard number of an arithmetic structure — An element of an arithmetic-language structure equal to the value of some standard numeral; this is structure-relative and does not assert that the domain element is literally a natural number. - **Medžuslovjansky:** `standardno čislo`; lemma `standardno čislo`; neuter adjective-noun phrase. - **Upotrěbljenje / inflection:** Neuter singular standardno čislo; instrumental plural standardnymi čislami. Add struktury M when the structure-relative sense could be missed. - **Kirilična forma:** `стандардно число` - **Argumentacija / rationale:** Standardno čislo is the transparent adjective-number phrase demanded by the definition. The use note keeps it distinct from a standard numeral, which is a syntactic term, and from a natural number, which is an external mathematical object. - **Uvěrjenost / status:** 0.93 (high); `provisional`; revision `OLISV-T0381-r0001`. - **Slovjanske sravnenja / comparanda:** ru: стандартное число; uk: стандартне число; pl: liczba standardowa; cs: standardní číslo; bcs: standardni broj; bg: стандартно число. - **Dokazy / evidence:** OL-MODEL-ARITHMETIC-NONSTANDARD-MODELS (lines 19-23); ISV-DICT-LIVE-20260825 (wordList[16187]; dictionary_id=20754; lemma=standardny); ISV-DICT-LIVE-20260825 (wordList[11893]; dictionary_id=17215; lemma=čislo; gloss=number); RU-MSU-GODEL-LECTURES-2020 (physical page 1 / extracted lines 58-67); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic, standard flavorization) - **Alternativy / alternatives:** standardny numeral: A numeral is the formal term whose value is the element; it is not the element itself.; prirodno čislo: An arbitrary structure's standard element need not literally be a natural number. - **Neizvěstnost / uncertainty:** Several national sources express this through the standard part or numeral values rather than a standalone positive phrase. ## OLISV-T0387 · arithmetic.sum-result - **English lemma / sense:** sum — The result of applying the interpreted addition operation to two elements, distinguished from the operation of addition itself. - **Medžuslovjansky:** `suma`; lemma `suma`; feminine noun. - **Upotrěbljenje / inflection:** Feminine singular suma; genitive sumy. Use dodavanje for the operation and suma for the resulting value. - **Kirilična forma:** `сума` - **Argumentacija / rationale:** Suma is a direct official head, maximally transparent across the comparison columns, and already occurs in an accepted arithmetic passage. Keeping it separate from canon head dodavanje preserves the operation/result distinction. - **Uvěrjenost / status:** 0.96 (high); `provisional`; revision `OLISV-T0387-r0001`. - **Slovjanske sravnenja / comparanda:** ru: сумма; uk: сума; pl: suma; cs: součet; suma; bcs: suma; zbroj; zbir; bg: сума; сбор. - **Dokazy / evidence:** OL-MODEL-ARITHMETIC-MODELS-Q (lines 52-60); ISV-DICT-LIVE-20260825 (wordList[16586]; dictionary_id=1427; lemma=suma; gloss=sum); OL-SIZE-PAIRING-ISV (line 33); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic, standard flavorization) - **Alternativy / alternatives:** zbir: A strong South-Slavic result term, but less even across the full comparison set than the official head suma.; dodavanje: Already canonized as the operation; using it for the result would erase the source's operation/result distinction. - **Neizvěstnost / uncertainty:** Czech and South-Slavic traditions also use native result nouns; the international form is selected for cross-regional transparency. ## OLISV-T0020 · computability.algorithm - **English lemma / sense:** algorithm — A finite effective procedure specifying steps for obtaining an output or solving a problem. - **Medžuslovjansky:** `algoritm`; lemma `algoritm`; masculine noun. - **Upotrěbljenje / inflection:** Masculine noun; genitive singular algoritma, nominative plural algoritmy. Use algoritm izčisljaje funkciju f for an effective procedure computing f. - **Kirilična forma:** `алгоритм` - **Argumentacija / rationale:** The dictionary and inherited corpus converge on a maximally recognizable international lemma with stable technical use across all comparison languages. - **Uvěrjenost / status:** 0.99 (high); `seed_preferred`; revision `OLISV-T0020-r0001`. - **Slovjanske sravnenja / comparanda:** ru: алгоритм; uk: алгоритм; pl: algorytm; cs: algoritmus; bcs: algoritam; bg: алгоритъм. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[579]; dictionary_id=23492); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** postupok: Postupok is useful for a generic procedure but does not by itself encode effectiveness or algorithmic formality. - **Neizvěstnost / uncertainty:** No specific uncertainty beyond the provisional edition boundary. ## OLISV-T0333 · computability.artificial-intelligence - **English lemma / sense:** artificial intelligence — The field of constructing or studying intelligent computational systems, named by the source as one home for investigations of nonclassical logics. - **Medžuslovjansky:** `umětna inteligencija`; lemma `umětna inteligencija`; feminine adjective-noun phrase. - **Upotrěbljenje / inflection:** Feminine inteligencija; genitive umětnoj inteligencije. - **Kirilična forma:** `умєтна интелигенција` - **Argumentacija / rationale:** Umětna inteligencija is the exact frozen full phrase and gives a readable Slavic counterpart rather than importing English AI. The source fixes only its role as a research rubric, not a comprehensive definition of the field. - **Uvěrjenost / status:** 0.99 (high); `provisional`; revision `OLISV-T0333-r0001`. - **Slovjanske sravnenja / comparanda:** ru: искусственный интеллект; uk: штучний інтелект; pl: sztuczna inteligencja; cs: umělá inteligence; bcs: umjetna inteligencija; вештачка интелигенција; bg: изкуствен интелект. - **Dokazy / evidence:** OL-FOL-BEYOND-OTHER-LOGICS (lines 33-36); ISV-DICT-LIVE-20260825 (dictionary_id=23046; lemma=umětna inteligencija; gloss=artificial intelligence); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** umětny intelekt: This East/South-oriented alternative is recognizable, but the frozen dictionary directly supplies the complete umětna inteligencija phrase with broad West/South support. - **Neizvěstnost / uncertainty:** National languages divide between intelligence and intellect heads; the directly frozen Interslavic phrase resolves the edition choice. ## OLISV-T0334 · computability.cognitive-science - **English lemma / sense:** cognitive science — The interdisciplinary study of cognition, named by the source as another field in which the introduced logical systems may be investigated. - **Medžuslovjansky:** `kognitivna nauka`; lemma `kognitivna nauka`; feminine adjective-noun phrase. - **Upotrěbljenje / inflection:** Feminine nauka; genitive kognitivnoj nauky. - **Kirilična forma:** `когнитивна наука` - **Argumentacija / rationale:** Kognitivna nauka preserves the widely shared international adjective and pairs it with the direct pan-Slavic nauka head. Its transparent composition is preferable to importing the English field name or forcing a narrower psychology label. - **Uvěrjenost / status:** 0.88 (high); `provisional`; revision `OLISV-T0334-r0001`. - **Slovjanske sravnenja / comparanda:** ru: когнитивная наука; uk: когнітивна наука; pl: kognitywistyka; nauka kognitywna; cs: kognitivní věda; bcs: kognitivna znanost; когнитивна наука; bg: когнитивна наука. - **Dokazy / evidence:** OL-FOL-BEYOND-OTHER-LOGICS (lines 33-36); ISV-DICT-LIVE-20260825 (dictionary_id=2005; lemma=nauka; gloss=science); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** nauka poznanja: A cognition-as-knowing paraphrase is too narrow for a field that also covers perception, language, memory, and computation. - **Neizvěstnost / uncertainty:** Polish often lexicalizes the discipline as kognitywistyka and Czech prefers věda; the Interslavic phrase is compositional rather than a claim of identical national naming. ## OLISV-T0023 · computability.computable - **English lemma / sense:** computable — Capable of being computed by an effective procedure in the chosen model of computation. - **Medžuslovjansky:** `izčislimy`; lemma `izčislimy`; hard adjective. - **Upotrěbljenje / inflection:** Derived editorially from perfective izčisliti using the second-conjugation present passive ending -imy. Inflect regularly: izčislima funkcija, izčislimo množstvo, izčislimy funkcije. - **Kirilična forma:** `изчислимы` - **Argumentacija / rationale:** Izčislimy is a regular, compact formation from the directly attested compute verb and parallels the East/South Slavic modal adjective pattern. Its lexicalized specialist meaning is useful but not directly listed, so it remains provisional. - **Uvěrjenost / status:** 0.66 (medium); `provisional`; revision `OLISV-T0023-r0001`. - **Slovjanske sravnenja / comparanda:** ru: вычислимый; uk: обчислюваний; pl: obliczalny; cs: vyčíslitelný; bcs: izračunljiv; bg: изчислим. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[2804]; dictionary_id=5879); ISV-GRAMMAR-VERBS (line 178); ISV-GRAMMAR-ADJ (lines 14-18); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** izčisljajemy: This regular imperfective present passive form means ‘being computed’ rather than the modal property ‘capable of computation’. - **Neizvěstnost / uncertainty:** No bounded official dictionary row directly attests izčislimy in the computability-theory sense.; The exact Ukrainian, Polish, Czech, BCS, and Bulgarian adjectives are editorial comparanda rather than values copied from the cited verbal-base row. ## OLISV-T0022 · computability.computation - **English lemma / sense:** computation — The process or result of calculating values according to an effective procedure. - **Medžuslovjansky:** `izčisljenje`; lemma `izčisljenje`; neuter verbal noun. - **Upotrěbljenje / inflection:** The dictionary source form izčisljeńje is normalized to standard/basic izčisljenje. Neuter noun; genitive singular izčisljenja. Use for a computational process or its result. - **Kirilična forma:** `изчисљење` - **Argumentacija / rationale:** The verbal noun is directly attested and strongly reinforced by inherited mathematical calculations; standardization only removes the optional soft-consonant diacritic. - **Uvěrjenost / status:** 0.9 (high); `seed_preferred`; revision `OLISV-T0022-r0001`. - **Slovjanske sravnenja / comparanda:** ru: вычисление; uk: розрахунок; pl: obliczenie; cs: výpočet; bcs: obračun; bg: изчисление. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[2808]; dictionary_id=3417); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** kalkulacija: Kalkulacija is highly recognizable but more readily suggests a numerical or commercial calculation and lacks the inherited fit of izčisljenje. - **Neizvěstnost / uncertainty:** The BCS dictionary columns favor obračun, which can carry a financial sense; this divergence is preserved in the comparanda. ## OLISV-T0335 · computability.computational-adjective - **English lemma / sense:** computational — Pertaining to computation, used by the source both for properties of a logic and for a primary motivation for introducing systems. - **Medžuslovjansky:** `izčisliteljny`; lemma `izčisliteljny`; adjective. - **Upotrěbljenje / inflection:** Masculine izčisliteljny, feminine izčisliteljna, neuter izčisliteljno, plural izčisliteljne. - **Kirilična forma:** `изчислитељны` - **Argumentacija / rationale:** Izčisliteljny transparently derives an adjective from the edition's established izčisljati/izčisljenje computation family and remains distinct from izčislimy, which means computable. The source needs the broader relational adjective for properties and motivation. - **Uvěrjenost / status:** 0.85 (high); `provisional`; revision `OLISV-T0335-r0001`. - **Slovjanske sravnenja / comparanda:** ru: вычислительный; uk: обчислювальний; pl: obliczeniowy; cs: výpočetní; bcs: računski; рачунски; bg: изчислителен. - **Dokazy / evidence:** OL-FOL-BEYOND-OTHER-LOGICS (lines 19-20 and 33-36); ISV-DICT-LIVE-20260825 (dictionary_id=5878; lemma=izčisljati; gloss=calculate, compute); ISV-DICT-LIVE-20260825 (dictionary_id=3417; lemma=izčisljeńje; gloss=calculation); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** izčislimy: Computable asserts that an object can be computed; computational only relates a property or motivation to computation, so substituting it would change the source's claim. - **Neizvěstnost / uncertainty:** The exact adjective is productively derived rather than a standalone frozen lemma, and national languages divide between calculation and computer-oriented roots. ## OLISV-T0021 · computability.compute - **English lemma / sense:** compute — To obtain the value of a function by an effective computational procedure. - **Medžuslovjansky:** `izčisljati`; lemma `izčisljati`; transitive imperfective verb. - **Upotrěbljenje / inflection:** Imperfective verb for the ongoing or general operation; perfective partner izčisliti for a completed computation. A function or algorithm is the grammatical subject and a value or function the object. - **Kirilična forma:** `изчисљати` - **Argumentacija / rationale:** Izčisljati is the only bounded dictionary verb explicitly glossed with compute and supplies a regular aspect partner for completed computations. - **Uvěrjenost / status:** 0.86 (high); `seed_preferred`; revision `OLISV-T0021-r0001`. - **Slovjanske sravnenja / comparanda:** ru: вычислять; uk: розраховувати; pl: obliczać; cs: počítat; bcs: računati, izračunavati; bg: изчислявам. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[2803]; dictionary_id=5878); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** kalkulovati: The international alternative is directly listed for calculate but is more readily associated with numerical or commercial calculation than general computability. - **Neizvěstnost / uncertainty:** The dictionary marks this lemma type 2 and shows weaker West/South intelligibility than the international kalkulovati; the specialist compute sense motivates the selection. ## OLISV-T0025 · computability.decidable - **English lemma / sense:** decidable — Computable as a set or relation, equivalently having an effective yes-or-no decision procedure. - **Medžuslovjansky:** `rěšimy`; lemma `rěšimy`; hard adjective. - **Upotrěbljenje / inflection:** Derived from rěšiti with the second-conjugation present passive ending -imy. Inflect regularly: rěšima relacija, rěšimo množstvo, rěšimy problemy. - **Kirilična forma:** `рєшимы` - **Argumentacija / rationale:** Rěšimy is morphologically regular, inherits a directly listed decide/determine base, and has an adjacent mathematical ‘solvable’ precedent in Noether. Open Logic’s definition fixes the algorithmic yes/no sense; the lexical extension stays provisional. - **Uvěrjenost / status:** 0.64 (medium); `provisional`; revision `OLISV-T0025-r0001`. - **Slovjanske sravnenja / comparanda:** ru: разрешимый; uk: розв'язний; pl: rozstrzygalny; cs: rozhodnutelný; bcs: odlučiv; bg: разрешим. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[4772]; dictionary_id=1256); ISV-GRAMMAR-VERBS (line 178); ISV-GRAMMAR-ADJ (lines 14-18); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** odlučimy: This would align more closely with BCS decide terminology but lacks the direct Interslavic base-row and inherited mathematical support available for rěšimy. - **Neizvěstnost / uncertainty:** No bounded official dictionary row attests rěšimy specifically for computability-theoretic decidability.; The six specialist comparison adjectives are editorial comparanda; their cited rows supply only verbal bases. ## OLISV-T0373 · computability.godel-number - **English lemma / sense:** Gödel number — The natural-number code assigned by a Gödel numbering to a syntactic object, here the code of a purported derivation of contradiction. - **Medžuslovjansky:** `Godelovo čislo`; lemma `Godelovo čislo`; neuter possessive-adjective noun phrase. - **Upotrěbljenje / inflection:** Use machine-canonical Godelovo čislo for indexing and Cyrillic projection; render the human Latin reader as G"odelovo čislo where TeX support preserves the name. Genitive Godelovogo čisla. - **Kirilična forma:** `Годелово число` - **Argumentacija / rationale:** Godelovo čislo combines the direct official čislo head with a Slavic possessive adjective. The Russian source directly attests the specialist phrase and proof-code sense, while Croatian independently supports the Gödelov possessive pattern. Machine data omits the umlaut for stable transliteration; the Latin TeX reader preserves Gödel's name typographically. - **Uvěrjenost / status:** 0.82 (high); `provisional`; revision `OLISV-T0373-r0001`. - **Slovjanske sravnenja / comparanda:** ru: гёделево число; uk: геделеве число; pl: liczba Gödla; cs: Gödelovo číslo; bcs: Gödelov broj; Геделов број; bg: Гьоделово число. - **Dokazy / evidence:** OL-MODEL-ARITHMETIC-INTRODUCTION (lines 64-71); ISV-DICT-LIVE-20260825 (wordList[11893]; dictionary_id=17215; lemma=čislo; gloss=number); RU-MSU-GODEL-LECTURES-2020 (physical page 8 / extracted lines 395-402 and 668-685); HR-ZAGREB-CLASSICAL-LOGIC-2013 (physical pages 66-69 / extracted lines 49-57); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic, standard flavorization) - **Alternativy / alternatives:** Godelov numer: Numer risks confusion with the syntactic numeral term and is less directly supported than the pan-Slavic number head čislo.; čislo Godela: The genitive phrase is understandable, but the possessive adjective matches the strongest Russian and Croatian specialist naming patterns and existing Slavic mathematical style. - **Neizvěstnost / uncertainty:** Only the Russian witness directly attests the full specialist concept in this packet.; Machine-canonical Godelovo and human-display Gödelovo are intentionally separate surfaces; this must remain explicit in indexes and TeX. ## OLISV-T0398 · computability.primitive-recursion - **English lemma / sense:** primitive recursion — The function-building operation defining a new function from base and recursive-step functions; in this unit it witnesses that successor, addition, and multiplication are computable. - **Medžuslovjansky:** `primitivna rekursija`; lemma `primitivna rekursija`; feminine adjective-noun phrase. - **Upotrěbljenje / inflection:** Primitivna agrees with feminine rekursija. Use s pomočju primitivnoj rekursije in the instrumental construction used by the translated passage. - **Kirilična forma:** `примитивна рекурсија` - **Argumentacija / rationale:** The compound keeps the active rekursija head, adds the directly dictionary-attested primitivny adjective, and is supported by direct Czech and Russian academic terminology. The translated prose states the logically safe direction: primitive-recursive arithmetic operations are therefore Turing-computable. - **Uvěrjenost / status:** 0.94 (high); `provisional`; revision `OLISV-T0398-r0001`. - **Slovjanske sravnenja / comparanda:** ru: примитивная рекурсия; uk: примітивна рекурсія; pl: rekursja pierwotna; cs: primitivní rekurze; bcs: primitivna rekurzija; примитивна рекурзија; bg: примитивна рекурсия. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[13417]; dictionary_id=35198; lemma=primitivny); OL-FOL-BEYOND-SECOND-ORDER-LOGIC (lines 153-157; active canon=OLISV-T0245-r0002); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic and standard flavorization) - **Alternativy / alternatives:** pervobytna rekursija: A literal everyday rendering of primitive is not the convergent specialist term and obscures recognition across the cited traditions.; primitivna rekurencija: Rekurencija follows Polish terminology but breaks the active Interslavic recursion head rekursija and the East/South cognate pattern. - **Neizvěstnost / uncertainty:** The South-Slavic and Ukrainian full phrases are componential comparisons in this evidence set rather than direct pinned quotations. ## OLISV-T0024 · computability.turing-machine - **English lemma / sense:** Turing machine — The abstract machine model that computes by state-governed operations on a tape. - **Medžuslovjansky:** `Turingova mašina`; lemma `Turingova mašina`; feminine noun phrase. - **Upotrěbljenje / inflection:** Mašina is the feminine head. Turingova is the nominative feminine singular possessive adjective in -ov and agrees with it; inflect both words as required by the clause. - **Kirilična forma:** `Турингова машина` - **Argumentacija / rationale:** The compound combines a directly attested, highly intelligible head with the official possessive-adjective pattern. It is concise and especially transparent to South Slavic readers, but remains provisional because the full eponym is not directly listed. - **Uvěrjenost / status:** 0.76 (medium); `provisional`; revision `OLISV-T0024-r0001`. - **Slovjanske sravnenja / comparanda:** ru: машина Тьюринга; uk: машина Тюрінга; pl: maszyna Turinga; cs: Turingův stroj; bcs: Turingov stroj / Turingova mašina; bg: машина на Тюринг. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[10605]; dictionary_id=2684); ISV-GRAMMAR-ADJ (lines 43-45); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** mašina Turinga: A genitive-name construction is understandable and closer to East/West usage, but the possessive adjective is the explicitly documented Interslavic pattern for a single-word masculine possessor. - **Neizvěstnost / uncertainty:** The full eponymic compound is constructed from documented components, not copied from an official terminology row.; Foreign-name handling in other publication pipelines may preserve Roman spelling; this record specifies the standard deterministic Cyrillic projection for this canon. ## OLISV-T0287 · computing.data-type - **English lemma / sense:** data type — A class of computational objects used to interpret a formula under the formulas-as-types paradigm. - **Medžuslovjansky:** `tip danych`; lemma `tip danych`; masculine noun with genitive plural. - **Upotrěbljenje / inflection:** Masculine tip; plural tipy danych, genitive tipa danych. - **Kirilična forma:** `тип даных` - **Argumentacija / rationale:** Tip danych directly composes the pinned type and data heads and matches the source's computational reading without conflating the term with the broader logical type entry. - **Uvěrjenost / status:** 0.98 (high); `provisional`; revision `OLISV-T0287-r0001`. - **Slovjanske sravnenja / comparanda:** ru: тип данных; uk: тип даних; pl: typ danych; cs: datový typ; bcs: tip podataka; тип података; bg: тип данни. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 108-112); ISV-DICT-LIVE-20260825 (dictionary_id=3224; lemma=tip; gloss=type, kind); ISV-DICT-LIVE-20260825 (dictionary_id=3548; lemma=dane; gloss=data); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** dany tip: This reverses the semantic relation and can be read as a given or specified type rather than a type of data. - **Neizvěstnost / uncertainty:** The entry is scoped to computational data types; the broader logical type remains T0256. ## OLISV-T0260 · function.application - **English lemma / sense:** function application — The operation of applying a function of type tau to an argument of type tau, yielding a value of the result type. - **Medžuslovjansky:** `aplikacija funkcije`; lemma `aplikacija funkcije`; feminine noun phrase. - **Upotrěbljenje / inflection:** Feminine aplikacija; genitive aplikacije funkcije. Reserve priměnjeńje for application of a method and keep this operation explicit. - **Kirilična forma:** `апликација функције` - **Argumentacija / rationale:** Aplikacija funkcije follows the target and the international application family for the formal operation, while the dictionary's priměnjeńje row is retained as an explicit adverse distinction for applying a method. The source's type rule fixes the specialist sense. - **Uvěrjenost / status:** 0.79 (medium); `provisional`; revision `OLISV-T0260-r0002`. - **Slovjanske sravnenja / comparanda:** ru: применение функции; uk: застосування функції; pl: zastosowanie funkcji; cs: aplikace funkce; bcs: primjena funkcije; примена функције; bg: прилагане на функция. - **Dokazy / evidence:** OL-FOL-BEYOND-HIGHER-ORDER-LOGIC (lines 29-32 and 65-67 and 108-110); ISV-DICT-LIVE-20260825 (dictionary_id=36574; lemma=aplikacija; gloss=application (software), app); ISV-DICT-LIVE-20260825 (dictionary_id=1289; lemma=funkcija; gloss=function); ISV-DICT-LIVE-20260825 (dictionary_id=35515; lemma=priměnjeńje; gloss=application (of a method)); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** priměnjeńje funkcije: The dictionary supports priměnjeńje for methods, but using it here would collapse operation-of-a-function with methodological application.; vyzov funkcije: A call/invocation term is narrower than the typed application operation in the source. - **Neizvěstnost / uncertainty:** The dictionary's direct aplikacija sense is software-oriented; the mathematical operation is an editorial extension supported by cross-Slavic usage.; The r0001 record is preserved as adverse provenance for the evidence correction. ## OLISV-T0050 · function.bijective - **English lemma / sense:** bijective function — A function that is both injective and surjective. - **Medžuslovjansky:** `bijektivna funkcija`; lemma `bijektivna funkcija`; noun phrase. - **Upotrěbljenje / inflection:** Feminine adjective agrees with funkcija; bijekcija may be used for the corresponding noun when context requires it. - **Kirilična forma:** `бијективна функција` - **Argumentacija / rationale:** Direct official function lemma and broad international specialist convergence, notwithstanding descriptive Polish usage. The English definition at OL-FUN-KINDS lines 112-116 fixes the intended sense; this revision selects an edition term without asserting official or native certification. - **Uvěrjenost / status:** 0.71 (medium); `provisional`; revision `OLISV-T0050-r0001`. - **Slovjanske sravnenja / comparanda:** ru: биективная функция; uk: бієктивна функція; pl: funkcja wzajemnie jednoznaczna; cs: bijektivní zobrazení; bcs: bijektivna funkcija; bg: биективна функция. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[7434]; dictionary_id=1289); ISV-GRAMMAR-ADJ (lines 14-18); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** vzajemno jednoznačna funkcija: The descriptive calque is clear in Polish and Russian traditions but longer and less morphologically uniform than bijektivna. - **Neizvěstnost / uncertainty:** No bounded official dictionary row directly attests bijektivna or bijekcija.; Cross-Slavic specialist surfaces are editorial comparanda from the bounded evidence review and are not represented as official or native-certified forms. ## OLISV-T0046 · function.codomain - **English lemma / sense:** codomain — The declared target set B of a function f from A to B. - **Medžuslovjansky:** `kodomena funkcije`; lemma `kodomena funkcije`; noun. - **Upotrěbljenje / inflection:** Kodomena is feminine; use kodomena as the short form and genitive funkcije when the governing function is named. - **Kirilična forma:** `кодомена функције` - **Argumentacija / rationale:** Direct official support for funkcija and wide specialist recognition of the international codomain stem, despite West Slavic calques. The English definition at OL-FUN-BASICS lines 28-40 fixes the intended sense; this revision selects an edition term without asserting official or native certification. - **Uvěrjenost / status:** 0.68 (medium); `provisional`; revision `OLISV-T0046-r0001`. - **Slovjanske sravnenja / comparanda:** ru: кодомен; uk: кодомен; pl: przeciwdziedzina; cs: cílová množina; bcs: kodomena; bg: кодомейн. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[7434]; dictionary_id=1289); ISV-GRAMMAR-ADJ (lines 14-18); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** protivdomena funkcije: The calque follows Polish but is less recognizable elsewhere than the international kodomena form. - **Neizvěstnost / uncertainty:** The official row supports funkcija only; kodomena itself is an editorial specialist selection.; Cross-Slavic specialist surfaces are editorial comparanda from the bounded evidence review and are not represented as official or native-certified forms. ## OLISV-T0009 · function.composition - **English lemma / sense:** composition — The function obtained by applying one function and then another in the specified order. - **Medžuslovjansky:** `kompozicija funkcij`; lemma `kompozicija`; feminine noun phrase. - **Upotrěbljenje / inflection:** Head noun kompozicija is feminine; genitive singular kompozicije. Use kompozicija funkcij f i g and preserve the source convention for the order in g ∘ f. - **Kirilična forma:** `композиција функциј` - **Argumentacija / rationale:** Kompozicija funkcij is immediately legible in East and South Slavic and keeps the operation distinct from addition. It is deliberately provisional because the bounded dictionary labels kompozicija only for music. - **Uvěrjenost / status:** 0.62 (medium); `provisional`; revision `OLISV-T0009-r0001`. - **Slovjanske sravnenja / comparanda:** ru: композиция функций; uk: композиція функцій; pl: złożenie funkcji; cs: skládání funkcí; bcs: kompozicija funkcija; bg: композиция на функции. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[3854]; dictionary_id=35582); ISV-DICT-LIVE-20260824 (wordList[7434]; dictionary_id=1289); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** složenje funkcij: This native-rooted option aligns better with Polish and Czech, but the inherited use of složenje is not an attestation of function composition and no direct dictionary noun row was found. - **Neizvěstnost / uncertainty:** No bounded official source directly selects between kompozicija funkcij and složenje funkcij for the mathematical operation. ## OLISV-T0272 · function.continuous - **English lemma / sense:** continuous function — A function introduced as a further mathematical object definable from the natural-number type in the higher-type framework. - **Medžuslovjansky:** `neprěryvna funkcija`; lemma `neprěryvna funkcija`; feminine noun phrase. - **Upotrěbljenje / inflection:** Feminine funkcija; plural neprěryvne funkcije, genitive neprěryvnoj funkcije. The direct dictionary lemma bezprěryvny is normalized to the edition's neprěryvny family. - **Kirilična forma:** `непрєрывна функција` - **Argumentacija / rationale:** The source names continuous functions as a canonical example, and the dictionary directly supplies the function head plus the bezprěryvny continuous family. Neprěryvna is an edition-level negative-prefix normalization, not a claim that the dictionary literally lists that surface. - **Uvěrjenost / status:** 0.94 (high); `provisional`; revision `OLISV-T0272-r0002`. - **Slovjanske sravnenja / comparanda:** ru: непрерывная функция; uk: неперервна функція; pl: funkcja ciągła; cs: spojitá funkce; bcs: neprekidna funkcija; непрекидна функција; bg: непрекъсната функция. - **Dokazy / evidence:** OL-FOL-BEYOND-HIGHER-ORDER-LOGIC (lines 114-117); ISV-DICT-LIVE-20260825 (dictionary_id=6536; lemma=bezprěryvny; gloss=continuous); ISV-DICT-LIVE-20260825 (dictionary_id=1289; lemma=funkcija; gloss=function); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** bezprěryvna funkcija: Literal dictionary spelling is preserved in evidence, but the target's neprěryvna normalization is consistent with the project-wide negative-prefix policy.; postojanna funkcija: Can mean constant or stationary and is not equivalent to continuity. - **Neizvěstnost / uncertainty:** National languages divide between continuous and unbroken roots; the selected normalized form is an edition preference, not a native certification.; The r0001 record is preserved as adverse provenance for the evidence correction. ## OLISV-T0008 · function.domain - **English lemma / sense:** domain — The set of admissible inputs of a function. - **Medžuslovjansky:** `domen funkcije`; lemma `domen`; masculine noun phrase. - **Upotrěbljenje / inflection:** Head noun domen is masculine; genitive singular domena. Use domen funkcije f when the function-theoretic sense is not already explicit. - **Kirilična forma:** `домен функције` - **Argumentacija / rationale:** The compact international lemma is directly attested in all six comparison columns and the added genitive funkcije fixes the intended input-set sense; the collocation remains provisional because the row is not sense-tagged. - **Uvěrjenost / status:** 0.74 (medium); `provisional`; revision `OLISV-T0008-r0001`. - **Slovjanske sravnenja / comparanda:** ru: домен; uk: домен; pl: domena; cs: doména; bcs: domena; bg: домейн. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[5559]; dictionary_id=36356); ISV-DICT-LIVE-20260824 (wordList[7434]; dictionary_id=1289); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** oblast oprědelenja funkcije: This descriptive East-Slavic-style phrase is semantically explicit but longer and has no direct bounded Interslavic attestation. - **Neizvěstnost / uncertainty:** Conventional terminology diverges sharply across Slavic languages; domen funkcije is a reversible editorial bridge, not an attested official collocation. ## OLISV-T0259 · function.functional - **English lemma / sense:** functional — A higher-type function whose arguments are themselves functions and whose result is a number or other object. - **Medžuslovjansky:** `funkcional`; lemma `funkcional`; masculine noun. - **Upotrěbljenje / inflection:** Plural funkcionaly; genitive funkcionala. The adjective funkcionaľny remains available when the source modifies another noun. - **Kirilična forma:** `функционал` - **Argumentacija / rationale:** The source uses functional as a noun for functions taking functions to numbers. Funkcional is a transparent derived noun from the direct funkcija/funkcionaľny family and preserves the target's plural funkcionaly. - **Uvěrjenost / status:** 0.82 (high); `provisional`; revision `OLISV-T0259-r0002`. - **Slovjanske sravnenja / comparanda:** ru: функционал; uk: функціонал; pl: funkcjonał; cs: funkcionál; bcs: funkcional; функционал; bg: функционал. - **Dokazy / evidence:** OL-FOL-BEYOND-HIGHER-ORDER-LOGIC (lines 34-38); ISV-DICT-LIVE-20260825 (dictionary_id=1289; lemma=funkcija; gloss=function); ISV-DICT-LIVE-20260825 (dictionary_id=35303; lemma=funkcionaľny; gloss=functional); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** funkcionaľny: This is an adjective in the pinned dictionary and cannot by itself name the higher-type object.; funkcija funkcij: Describes a general function between function spaces but loses the specialist functional noun used by the source. - **Neizvěstnost / uncertainty:** The noun is derived rather than directly listed; national traditions alternate functional, functional, and operator terminology.; The r0001 record is preserved as adverse provenance for the evidence correction. ## OLISV-T0051 · function.graph - **English lemma / sense:** graph of a function — The relation of ordered pairs x,y such that f(x) equals y. - **Medžuslovjansky:** `graf funkcije`; lemma `graf funkcije`; noun phrase. - **Upotrěbljenje / inflection:** Graf is masculine; use genitive singular funkcije. This relational graph is distinct from an illustrative plot unless context identifies them. - **Kirilična forma:** `граф функције` - **Argumentacija / rationale:** Direct function component and broad recognition of graf or its close derivative, with a deliberate relation-versus-plot distinction. The English definition at OL-FUN-RELATIONS lines 24-30 fixes the intended sense; this revision selects an edition term without asserting official or native certification. - **Uvěrjenost / status:** 0.67 (medium); `provisional`; revision `OLISV-T0051-r0001`. - **Slovjanske sravnenja / comparanda:** ru: график функции; uk: графік функції; pl: wykres funkcji; cs: graf funkce; bcs: graf funkcije; bg: графика на функция. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[7434]; dictionary_id=1289); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** grafik funkcije: Grafik can suggest a plotted curve, while the Open Logic definition treats the graph extensionally as a relation. - **Neizvěstnost / uncertainty:** No bounded official row directly attests graf funkcije in this extensional sense.; Cross-Slavic specialist surfaces are editorial comparanda from the bounded evidence review and are not represented as official or native-certified forms. ## OLISV-T0054 · function.image-of-set - **English lemma / sense:** image of a set under a function — For C in the domain of f, the set of all values f(x) with x in C. - **Medžuslovjansky:** `obraz množstva pri funkciji`; lemma `obraz množstva pri funkciji`; noun phrase. - **Upotrěbljenje / inflection:** Obraz is masculine; use genitive singular množstva and locative singular funkciji after pri. - **Kirilična forma:** `образ множства при функцији` - **Argumentacija / rationale:** Direct function component, inherited mathematical mapping uses of obraz, and strong East/West/Bulgarian comparison support. The English definition at OL-FUN-RELATIONS lines 78-90 fixes the intended sense; this revision selects an edition term without asserting official or native certification. - **Uvěrjenost / status:** 0.7 (medium); `provisional`; revision `OLISV-T0054-r0001`. - **Slovjanske sravnenja / comparanda:** ru: образ множества; uk: образ множини; pl: obraz zbioru; cs: obraz množiny; bcs: slika skupa; bg: образ на множество. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[7434]; dictionary_id=1289); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** priměnjenje funkcije na množstvo: The source permits application terminology, but obraz is shorter and distinguishes the resulting set from the operation. - **Neizvěstnost / uncertainty:** BCS commonly prefers slika, and no bounded official row attests the complete phrase.; Cross-Slavic specialist surfaces are editorial comparanda from the bounded evidence review and are not represented as official or native-certified forms. ## OLISV-T0048 · function.injective - **English lemma / sense:** injective function — A function for which every codomain element has at most one preimage. - **Medžuslovjansky:** `injektivna funkcija`; lemma `injektivna funkcija`; noun phrase. - **Upotrěbljenje / inflection:** Feminine adjective agrees with funkcija; the adjective alone may be used predicatively when the function is explicit. - **Kirilična forma:** `инјективна функција` - **Argumentacija / rationale:** Direct official function lemma, regular adjective agreement, and strong international recognition in East and South Slavic. The English definition at OL-FUN-KINDS lines 64-68 fixes the intended sense; this revision selects an edition term without asserting official or native certification. - **Uvěrjenost / status:** 0.68 (medium); `provisional`; revision `OLISV-T0048-r0002`. - **Slovjanske sravnenja / comparanda:** ru: инъективная функция; uk: ін'єктивна функція; pl: funkcja różnowartościowa; cs: prostá funkce; bcs: injektivna funkcija; bg: инективна функция. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[7434]; dictionary_id=1289); ISV-GRAMMAR-ADJ (lines 14-18); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** jedno-jednoznačna funkcija: The descriptive alternative is cross-Slavically uneven and longer; injektivna is concise and internationally recognizable. - **Neizvěstnost / uncertainty:** Polish and Czech favor native descriptive terminology, and no official row attests the complete Interslavic compound.; Cross-Slavic specialist surfaces are editorial comparanda from the bounded evidence review and are not represented as official or native-certified forms. ## OLISV-T0052 · function.inverse - **English lemma / sense:** inverse function — A function g that undoes f on both sides: f(g(y)) equals y and g(f(x)) equals x. - **Medžuslovjansky:** `obratna funkcija`; lemma `obratna funkcija`; noun phrase. - **Upotrěbljenje / inflection:** Feminine adjective agrees with funkcija; instrumental singular is obratnoju funkcijeju and accusative singular obratnu funkciju. - **Kirilična forma:** `обратна функција` - **Argumentacija / rationale:** Direct official function component, transparent native adjective, and strong comparison-language support for the selected or synonymous inverse stem. The English definition at OL-FUN-INVERSES lines 27-33 fixes the intended sense; this revision selects an edition term without asserting official or native certification. - **Uvěrjenost / status:** 0.74 (medium); `provisional`; revision `OLISV-T0052-r0001`. - **Slovjanske sravnenja / comparanda:** ru: обратная функция; uk: обернена функція; pl: funkcja odwrotna; cs: inverzní funkce; bcs: inverzna funkcija; bg: обратна функция. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[7434]; dictionary_id=1289); ISV-GRAMMAR-ADJ (lines 14-18); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** inverzna funkcija: The international form is strong in Czech and BCS, but obratna maximizes immediate East Slavic and Bulgarian transparency. - **Neizvěstnost / uncertainty:** The complete compound lacks a direct bounded official dictionary attestation.; Cross-Slavic specialist surfaces are editorial comparanda from the bounded evidence review and are not represented as official or native-certified forms. ## OLISV-T0007 · function.mathematical - **English lemma / sense:** function — A mapping assigning each element of a domain exactly one value in a codomain. - **Medžuslovjansky:** `funkcija`; lemma `funkcija`; feminine noun. - **Upotrěbljenje / inflection:** Feminine noun; genitive singular funkcije, nominative plural funkcije. Write funkcija f iz A v B for f: A → B. - **Kirilična forma:** `функција` - **Argumentacija / rationale:** The lemma is directly listed, essentially identical across the comparison languages, and deeply established in the inherited mathematical corpus. - **Uvěrjenost / status:** 0.99 (high); `seed_preferred`; revision `OLISV-T0007-r0001`. - **Slovjanske sravnenja / comparanda:** ru: функция; uk: функція; pl: funkcja; cs: funkce; bcs: funkcija; bg: функция. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[7434]; dictionary_id=1289); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** odobraženje: This can express a mapping, but it is narrower and less stable as the general headword for all Open Logic functions. - **Neizvěstnost / uncertainty:** No specific uncertainty beyond the provisional edition boundary. ## OLISV-T0261 · function.projection - **English lemma / sense:** projection — The operation selecting a component of a tuple or product object, such as p1 or p2. - **Medžuslovjansky:** `projekcija`; lemma `projekcija`; feminine noun. - **Upotrěbljenje / inflection:** Feminine projekcija; plural projekcije, genitive projekcije. Use the same head for tuple projections and deterministic script projection only when qualified. - **Kirilična forma:** `пројекција` - **Argumentacija / rationale:** Projekcija is directly listed with the same mathematical sense and exactly names the p1/p2 operations in the source. The canon keeps the function-domain sense distinct from the unrelated Cyrillic projection mechanism by context. - **Uvěrjenost / status:** 0.98 (high); `provisional`; revision `OLISV-T0261-r0002`. - **Slovjanske sravnenja / comparanda:** ru: проекция; uk: проєкція; pl: projekcja; cs: projekce; bcs: projekcija; пројекција; bg: проекция. - **Dokazy / evidence:** OL-FOL-BEYOND-HIGHER-ORDER-LOGIC (lines 49-55 and 70-82); ISV-DICT-LIVE-20260825 (dictionary_id=5651; lemma=projekcija; gloss=projection); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** izbor komponenty: Describes the result informally and loses the established operation name.; odraz: Can mean reflection or image and is semantically ambiguous in this product-type context. - **Neizvěstnost / uncertainty:** National mathematical usage alternates projection and component map; the direct dictionary head gives the edition a stable international form.; The r0001 record is preserved as adverse provenance for the evidence correction. ## OLISV-T0047 · function.range - **English lemma / sense:** range of a function — The subset of the codomain consisting of values attained by a function. - **Medžuslovjansky:** `obraz funkcije`; lemma `obraz funkcije`; noun phrase. - **Upotrěbljenje / inflection:** Obraz is masculine; use genitive singular funkcije. Do not confuse the attained range with the declared kodomena. - **Kirilična forma:** `образ функције` - **Argumentacija / rationale:** Direct function component and inherited mapping uses of the obraz stem, with substantial lexical divergence among comparanda. The English definition at OL-FUN-BASICS lines 38-40 fixes the intended sense; this revision selects an edition term without asserting official or native certification. - **Uvěrjenost / status:** 0.66 (medium); `provisional`; revision `OLISV-T0047-r0001`. - **Slovjanske sravnenja / comparanda:** ru: область значений; uk: область значень; pl: zbiór wartości; cs: obor hodnot; bcs: slika funkcije; bg: образ на функция. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[7434]; dictionary_id=1289); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** oblast vrednostij: The descriptive alternative is clear but longer; obraz aligns with the edition's mapping vocabulary and South/Bulgarian mathematical usage. - **Neizvěstnost / uncertainty:** No bounded official row attests obraz specifically for the range of a function.; Cross-Slavic specialist surfaces are editorial comparanda from the bounded evidence review and are not represented as official or native-certified forms. ## OLISV-T0053 · function.restriction - **English lemma / sense:** restriction of a function — The function obtained by limiting a function's domain to a subset while retaining its values. - **Medžuslovjansky:** `ograničenje funkcije`; lemma `ograničenje funkcije`; noun phrase. - **Upotrěbljenje / inflection:** Ograničenje is neuter; use genitive singular funkcije and specify the restricted subset with na plus accusative. - **Kirilična forma:** `ограничење функције` - **Argumentacija / rationale:** Direct function component and transparent Slavic restriction morphology, with marked terminology divergence in Ukrainian, Polish, Czech, and BCS. The English definition at OL-FUN-RELATIONS lines 78-86 fixes the intended sense; this revision selects an edition term without asserting official or native certification. - **Uvěrjenost / status:** 0.63 (medium); `provisional`; revision `OLISV-T0053-r0001`. - **Slovjanske sravnenja / comparanda:** ru: ограничение функции; uk: звуження функції; pl: obcięcie funkcji; cs: restrikce funkce; bcs: restrikcija funkcije; bg: ограничение на функция. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[7434]; dictionary_id=1289); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** restrikcija funkcije: The international form is strong in Czech and BCS, but ograničenje is directly understandable in East and South Slavic and fixed in the edition. - **Neizvěstnost / uncertainty:** The exact specialist compound is editorial and not directly attested in the bounded official evidence.; Cross-Slavic specialist surfaces are editorial comparanda from the bounded evidence review and are not represented as official or native-certified forms. ## OLISV-T0049 · function.surjective - **English lemma / sense:** surjective function — A function whose range equals its codomain. - **Medžuslovjansky:** `surjektivna funkcija`; lemma `surjektivna funkcija`; noun phrase. - **Upotrěbljenje / inflection:** Feminine adjective agrees with funkcija; the adjective alone may be used predicatively when the function is explicit. - **Kirilična forma:** `сурјективна функција` - **Argumentacija / rationale:** Direct official function lemma and international recognition in East and South Slavic, with divergent Polish and Czech conventions. The English definition at OL-FUN-KINDS lines 29-37 fixes the intended sense; this revision selects an edition term without asserting official or native certification. - **Uvěrjenost / status:** 0.67 (medium); `provisional`; revision `OLISV-T0049-r0001`. - **Slovjanske sravnenja / comparanda:** ru: сюръективная функция; uk: сюр'єктивна функція; pl: funkcja na; cs: zobrazení na; bcs: surjektivna funkcija; bg: сюрективна функция. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[7434]; dictionary_id=1289); ISV-GRAMMAR-ADJ (lines 14-18); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** funkcija na: The short native construction is established in Polish and Czech but is syntactically opaque across the full comparison set. - **Neizvěstnost / uncertainty:** The specialist adjective is editorial and lacks a direct bounded official dictionary row.; Cross-Slavic specialist surfaces are editorial comparanda from the bounded evidence review and are not represented as official or native-certified forms. ## OLISV-T0139 · functions.successor-function - **English lemma / sense:** successor function — The arithmetic function sending each natural number to its immediate successor. - **Medžuslovjansky:** `funkcija naslědnika`; lemma `funkcija naslědnika`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive funkcije naslědnika; distinguish the mathematical function from the postfix function symbol used to denote it. - **Kirilična forma:** `функција наслєдника` - **Argumentacija / rationale:** The compound reuses the canonical function term and a direct successor lemma transparent across South Slavic and related national specialist forms. - **Uvěrjenost / status:** 0.82 (medium); `provisional`; revision `OLISV-T0139-r0001`. - **Slovjanske sravnenja / comparanda:** ru: функция следования; uk: функція наступника; pl: funkcja następnika; cs: následnická funkce; bcs: funkcija nasljednika; функција наследника; bg: функция на наследника. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[7434]; dictionary_id=1289); ISV-DICT-LIVE-20260825 (wordList[16538]; dictionary_id=9462); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** slědujuća funkcija: The adjective can suggest the next function in a list rather than the function mapping an argument to its successor. - **Neizvěstnost / uncertainty:** Russian often uses funkcija sledovanija rather than a successor noun compound. ## OLISV-T0250 · graph.connectedness - **English lemma / sense:** graph connectedness — The property that a graph has no non-trivial separation of its vertices into parts with no crossing edge. - **Medžuslovjansky:** `povezanost grafov`; lemma `povezanost grafov`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive povezanosti grafov; use povezaně grafy for the corresponding adjective phrase. - **Kirilična forma:** `повезаност графов` - **Argumentacija / rationale:** Povezanost is the transparent South/East-Slavic nominalization of the connected relation, and graf is already an international mathematical stem. The source's one-direction edge formula is preserved as written and not silently strengthened. - **Uvěrjenost / status:** 0.73 (medium); `provisional`; revision `OLISV-T0250-r0002`. - **Slovjanske sravnenja / comparanda:** ru: связность графа; uk: зв'язність графа; pl: spójność grafu; cs: souvislost grafu; bcs: povezanost grafa; повезаност графа; bg: свързаност на граф. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (dictionary_id=35684; lemma=grafičny; gloss=graphic); ISV-DICT-LIVE-20260825 (dictionary_id=3512; lemma=svęzany; gloss=connected, related); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** sȯedinjenje grafov: Suggests a construction joining graphs, not an internal graph property.; konečnost grafov: Confuses connectedness with finiteness. - **Neizvěstnost / uncertainty:** The source formula only blocks one directed crossing orientation; this record names the intended prose notion while preserving that adverse formal boundary.; The r0001 record remains preserved as adverse provenance for the target/source locator mismatch. ## OLISV-T0131 · logic.abbreviation - **English lemma / sense:** abbreviation — A notation introduced as a shorter written surrogate for a fully specified expression. - **Medžuslovjansky:** `skraćenje`; lemma `skraćenje`; neuter noun. - **Upotrěbljenje / inflection:** Genitive skraćenja; verb skraćati; distinguish an abbreviation convention from a defined object-language symbol where necessary. - **Kirilična forma:** `скрачење` - **Argumentacija / rationale:** The noun is the regular derivation from the direct dictionary verb skraćati and balances East, West and South Slavic shortening roots. - **Uvěrjenost / status:** 0.78 (medium); `provisional`; revision `OLISV-T0131-r0001`. - **Slovjanske sravnenja / comparanda:** ru: сокращение; uk: скорочення; pl: skrót; cs: zkratka; bcs: skraćenje; скраћење; bg: съкращение. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[15357]; dictionary_id=3139); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** sokraćenje: The prothetic form is East-facing but less aligned with the direct dictionary head and the established skrać- family. - **Neizvěstnost / uncertainty:** The frozen dictionary attests the verb rather than this exact noun. ## OLISV-T0309 · logic.accessibility-relation - **English lemma / sense:** accessibility relation — The binary relation R between worlds that determines which worlds must be considered from a given world. - **Medžuslovjansky:** `odnošenje dostųpnosti`; lemma `odnošenje dostųpnosti`; neuter noun phrase. - **Upotrěbljenje / inflection:** Neuter odnošenje; genitive odnošenja dostųpnosti. Use dostųpny for a world reachable under the relation. - **Kirilična forma:** `одношење доступности` - **Argumentacija / rationale:** Odnošenje dostųpnosti combines the direct relation and accessibility families and states the source's world-to-world role without importing a national spelling. The compatibility gloss is retained as an interpretation, not as a redefinition of R. - **Uvěrjenost / status:** 0.91 (high); `provisional`; revision `OLISV-T0309-r0001`. - **Slovjanske sravnenja / comparanda:** ru: отношение достижимости; uk: відношення досяжності; pl: relacja dostępności; cs: relace dosažitelnosti; bcs: relacija dostupnosti; bg: отношение на достижимост. - **Dokazy / evidence:** OL-FOL-BEYOND-MODAL-LOGICS (lines 43-48 and 81-89); ISV-DICT-LIVE-20260825 (dictionary_id=1992; lemma=odnošeńje; gloss=relation, relationship); ISV-DICT-LIVE-20260825 (dictionary_id=6045; lemma=dostųpnosť; gloss=accessibility); ISV-DICT-LIVE-20260825 (dictionary_id=3054; lemma=dostųpny; gloss=accessible, reachable); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** odnošenje sovmestnosti: Compatibility is one intuitive reading of R(p,q), but the source also uses reflexive, transitive, and universal restrictions; accessibility names the wider formal role. - **Neizvěstnost / uncertainty:** The exact national technical noun varies between accessibility and reachability families; no native certification is claimed for the compound. ## OLISV-T0142 · logic.ambiguous-formula - **English lemma / sense:** ambiguous formula — A symbol string admitted as a formula that has more than one syntactic parse under the formation rules. - **Medžuslovjansky:** `nejednoznačna formula`; lemma `nejednoznačna formula`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive nejednoznačnoj formuly; reserve this term for syntactic ambiguity, not semantic underdetermination. - **Kirilična forma:** `неједнозначна формула` - **Argumentacija / rationale:** The transparent negation of canonical jednoznačna directly marks failure of unique parsing and avoids the semantic overtones of a two-meaning adjective. - **Uvěrjenost / status:** 0.88 (high); `provisional`; revision `OLISV-T0142-r0001`. - **Slovjanske sravnenja / comparanda:** ru: неоднозначная формула; uk: неоднозначна формула; pl: formuła niejednoznaczna; cs: nejednoznačná formule; bcs: nejednoznačna formula; неједнозначна формула; bg: нееднозначна формула. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[6530]; dictionary_id=17625); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** dvusmyslena formula: The alternative can suggest two semantic meanings rather than two syntactic constructions. - **Neizvěstnost / uncertainty:** The negative compound is regularly derived rather than directly listed in the frozen dictionary. ## OLISV-T0302 · logic.antecedent - **English lemma / sense:** antecedent — The condition or first component of a conditional assertion, written A in the source's material and modal discussion. - **Medžuslovjansky:** `prědhodna čest`; lemma `prědhodna čest`; feminine adjective-noun phrase. - **Upotrěbljenje / inflection:** Feminine čest; use prědhodnoj česti in the genitive and prědhodnoju čestju in the instrumental. - **Kirilična forma:** `прєдходна чест` - **Argumentacija / rationale:** Prědhodna čest is a transparent native compound: the precedence adjective identifies the first component and čest keeps the part/portion sense visible. The formal source context, not a claim of national textbook identity, fixes it as antecedent. - **Uvěrjenost / status:** 0.76 (medium); `provisional`; revision `OLISV-T0302-r0001`. - **Slovjanske sravnenja / comparanda:** ru: антецедент; условие; uk: антецедент; попередня частина; pl: poprzednik; cs: antecedent; předpoklad; bcs: antecedent; prethodnik; bg: антецедент; условие. - **Dokazy / evidence:** OL-FOL-BEYOND-MODAL-LOGICS (lines 20-25); ISV-DICT-LIVE-20260825 (dictionary_id=14924; lemma=prědhodny; gloss=previous); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** antecedent: The international loan is searchable but less immediately parsable for readers who rely on the shared prěd- and čest families. - **Neizvěstnost / uncertainty:** The complete compound is editorial; in some traditions antecedent is treated as the condition itself rather than a syntactic component. ## OLISV-T0233 · logic.argument-position - **English lemma / sense:** argument position — One ordered input slot of a function or relation, assigned a specified sort in a many-sorted signature. - **Medžuslovjansky:** `pozicija argumenta`; lemma `pozicija argumenta`; feminine noun phrase with genitive singular. - **Upotrěbljenje / inflection:** Genitive pozicije argumenta; plural pozicije argumentov. - **Kirilična forma:** `позиција аргумента` - **Argumentacija / rationale:** Two direct international components make the ordered formal slot transparent across all comparison traditions. - **Uvěrjenost / status:** 0.95 (high); `provisional`; revision `OLISV-T0233-r0001`. - **Slovjanske sravnenja / comparanda:** ru: позиция аргумента; uk: позиція аргументу; pl: pozycja argumentu; cs: pozice argumentu; bcs: pozicija argumenta; позиција аргумента; bg: позиция на аргумента. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[1079]; dictionary_id=19638; lemma=argument; gloss=argument); ISV-DICT-LIVE-20260825 (wordList[13187]; dictionary_id=1225; lemma=pozicija; gloss=position); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** město argumenta: Understandable but less specifically terminological.; poredok argumenta: Names order rather than one slot within the order. - **Neizvěstnost / uncertainty:** The direct components are stable, while national specialist traditions vary in case government and term order. ## OLISV-T0121 · logic.arity - **English lemma / sense:** arity — The fixed number of arguments taken by a predicate or function symbol. - **Medžuslovjansky:** `městnost`; lemma `městnost`; feminine noun. - **Upotrěbljenje / inflection:** Genitive městnosti; prefer jednoměstny, dvoměstny, and n-městny for logical argument count. Retain unarny/binarny as searchable international aliases and accepted legacy surfaces. - **Kirilična forma:** `мєстност` - **Argumentacija / rationale:** The transparent place-count family remains preferred and is already used throughout the accepted first-order text. The source and accepted earlier pages also expose unary/binary international variants, which are recorded as aliases rather than competing heads. - **Uvěrjenost / status:** 0.76 (high); `provisional`; revision `OLISV-T0121-r0002`. - **Slovjanske sravnenja / comparanda:** ru: арность; местность; uk: арність; місцевість; pl: arność; cs: arita; četnost míst; bcs: arnost; арност; bg: арност. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** arnost: The international calque is concise but is less broadly transparent in ordinary Slavic reading.; unarnost/binarnost: Recognizable international aliases, but less productive and less internally consistent than the established -městny family. - **Neizvěstnost / uncertainty:** National traditions split between arity loans, place-count descriptions, and unary/binary international adjectives. ## OLISV-T0101 · logic.atomic-formula - **English lemma / sense:** atomic formula — A formula containing no logical connective or quantifier and built directly from predicate symbols and terms, or identity. - **Medžuslovjansky:** `atomarna formula`; lemma `atomarna formula`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive atomarnoj formuly; use atomarna for the formal-logical category. - **Kirilična forma:** `атомарна формула` - **Argumentacija / rationale:** Atomarna follows the dominant East and South specialist pattern and remains transparent beside West-Slavic atomowa/atomická. - **Uvěrjenost / status:** 0.77 (medium); `provisional`; revision `OLISV-T0101-r0001`. - **Slovjanske sravnenja / comparanda:** ru: атомарная формула; uk: атомарна формула; pl: formuła atomowa; cs: atomická formule; bcs: atomarna formula; атомарна формула; bg: атомарна формула. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[1337]; dictionary_id=4661); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** atomna formula: The shorter adjective is widespread in the inherited draft but more readily evokes physical atoms; retain it as an adverse historical variant. - **Neizvěstnost / uncertainty:** No frozen dictionary row directly attests the complete logical compound.; Earlier accepted units use atomna formula and may require a later monotonic normalization decision. ## OLISV-T0012 · logic.axiom - **English lemma / sense:** axiom — A sentence adopted as a starting assumption of a formal theory or axiom system. - **Medžuslovjansky:** `aksioma`; lemma `aksioma`; feminine noun. - **Upotrěbljenje / inflection:** Feminine noun; genitive singular aksiomy, nominative plural aksiomy. Use sistema aksiom or aksiomatična teorija for the surrounding system. - **Kirilična forma:** `аксиома` - **Argumentacija / rationale:** Aksioma has direct dictionary support in every comparison language and exact inherited use as a formal mathematical assumption. - **Uvěrjenost / status:** 0.98 (high); `seed_preferred`; revision `OLISV-T0012-r0001`. - **Slovjanske sravnenja / comparanda:** ru: аксиома; uk: аксіома; pl: aksjomat; cs: axiom; bcs: aksiom; bg: аксиома. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[1498]; dictionary_id=24180); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** postulat: Postulat is recognizable but can carry a methodological nuance distinct from a formal axiom and lacks equally direct bounded evidence here. - **Neizvěstnost / uncertainty:** No specific uncertainty beyond the provisional edition boundary. ## OLISV-T0227 · logic.axiom-infinity - **English lemma / sense:** axiom of infinity — The named axiom of infinity introduced in the Principia system and cited here without a formal statement as an example that may not appear purely logical. - **Medžuslovjansky:** `aksioma bezkonečnosti`; lemma `aksioma bezkonečnosti`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive aksiomy bezkonečnosti. The source names but does not formulate the axiom; do not infer a particular set-theoretic or type-theoretic formulation without context. - **Kirilična forma:** `аксиома безконечности` - **Argumentacija / rationale:** The named historical axiom merits a dedicated searchable head. It reuses the direct axiom lemma and the edition's established bezkoneč- infinity family while preserving national ne-/bes-/bezkray- alternatives as comparanda. The frozen row's etymological bezkonėč- is explicitly normalized to the edition's standard bezkoneč- surface rather than misquoted as an exact lemma. - **Uvěrjenost / status:** 0.9 (high); `provisional`; revision `OLISV-T0227-r0001`. - **Slovjanske sravnenja / comparanda:** ru: аксиома бесконечности; uk: аксіома нескінченності; pl: aksjomat nieskończoności; cs: axiom nekonečna; bcs: aksiom beskonačnosti; аксиом бесконачности; bg: аксиома за безкрайност. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[1498]; dictionary_id=24180; lemma=aksioma; gloss=axiom); ISV-DICT-LIVE-20260825 (wordList[6136]; dictionary_id=6520; lemma=bezkonėčny; gloss=endless, infinite, perpetual); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** aksioma nekonečnosti: A strong West-Slavic and Ukrainian-family alternative, but it conflicts with the lane's established bezkoneč- infinity head. - **Neizvěstnost / uncertainty:** The source names but does not formulate the axiom, so the entry does not choose among historical or modern formal versions.; The frozen row attests etymological bezkonėčny; selected bezkoneč- is the edition/flavor-normalized surface. ## OLISV-T0228 · logic.axiom-reducibility - **English lemma / sense:** axiom of reducibility — The historically specific Principia axiom of reducibility, cited here without formulation among axioms that by most standards do not appear purely logical. - **Medžuslovjansky:** `aksioma reducibilnosti`; lemma `aksioma reducibilnosti`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive aksiomy reducibilnosti. Reserve the compound for the Russell-Whitehead historical axiom rather than generic reducibility claims. - **Kirilična forma:** `аксиома редуцибилности` - **Argumentacija / rationale:** The historically specific name warrants a separate entry. Reducibilnost is the most transparent international compromise across the six traditions; the much stronger East- and West-Slavic native derivations remain visible as adverse comparison evidence. - **Uvěrjenost / status:** 0.67 (medium); `provisional`; revision `OLISV-T0228-r0001`. - **Slovjanske sravnenja / comparanda:** ru: аксиома сводимости; uk: аксіома зведення; аксіома редукованості; pl: aksjomat sprowadzalności; cs: axiom reducibility; axiom redukovatelnosti; bcs: aksiom reducibilnosti; аксиом редуцибилности; bg: аксиома за редуцируемост. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[1498]; dictionary_id=24180; lemma=aksioma; gloss=axiom); ISV-DICT-LIVE-20260825 (wordList[14072]; dictionary_id=30601; lemma=redukcija; gloss=reduction); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** aksioma svodimosti: The East-Slavic form is precise but weakly transparent across West and South Slavic traditions and lacks direct Interslavic lexical support. - **Neizvěstnost / uncertainty:** The frozen dictionary's redukcija row does not directly attest reducibilnost or the Russell-Whitehead sense.; Czech and Ukrainian historical terminology varies between international and native derivations. ## OLISV-T0289 · logic.axiom-schema - **English lemma / sense:** axiom schema — A pattern whose substitution instances are axioms of a deductive system. - **Medžuslovjansky:** `shema aksiom`; lemma `shema aksiom`; feminine noun with genitive plural. - **Upotrěbljenje / inflection:** Feminine shema; plural shemy aksiom, genitive shemy aksiom. - **Kirilična forma:** `схема аксиом` - **Argumentacija / rationale:** Shema aksiom directly composes the pinned heads and preserves the source's distinction between a schema and its individual instances. - **Uvěrjenost / status:** 0.97 (high); `provisional`; revision `OLISV-T0289-r0001`. - **Slovjanske sravnenja / comparanda:** ru: схема аксиом; uk: схема аксіом; pl: schemat aksjomatu; cs: schéma axiomu; bcs: shema aksioma; схема аксиома; bg: схема от аксиоми. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 117-133); ISV-DICT-LIVE-20260825 (dictionary_id=18814; lemma=shema; gloss=scheme); ISV-DICT-LIVE-20260825 (dictionary_id=24180; lemma=aksioma; gloss=axiom); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** aksiomatična shema: The adjectival form is possible but makes the axiom/schema relation less explicit for readers across language traditions. - **Neizvěstnost / uncertainty:** National number marking varies between singular and plural axiom complements; the canon chooses a transparent genitive plural. ## OLISV-T0082 · logic.axiomatic-method - **English lemma / sense:** axiomatic method — The method of describing a class of structures by sentences taken as the axioms of a theory. - **Medžuslovjansky:** `aksiomatična metoda`; lemma `aksiomatična metoda`; feminine noun phrase. - **Upotrěbljenje / inflection:** The dictionary head is feminine metoda; use genitive aksiomatičnoj metody and instrumental aksiomatičnoju metodoju. - **Kirilična forma:** `аксиоматична метода` - **Argumentacija / rationale:** Both components are direct headwords; the feminine head follows frozen Interslavic usage while the national masculine split remains visible. - **Uvěrjenost / status:** 0.91 (high); `provisional`; revision `OLISV-T0082-r0001`. - **Slovjanske sravnenja / comparanda:** ru: аксиоматический метод; uk: аксіоматичний метод; аксіоматична метода; pl: metoda aksjomatyczna; cs: axiomatická metoda; bcs: aksiomatička metoda; bg: аксиоматичен метод. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[1499], wordList[11022]; dictionary_id=37533,2867); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** aksiomatičny metod: Recognizable but conflicts with the selected feminine dictionary headword.; aksiomna metoda: Shorter but not directly attested as the named methodology. - **Neizvěstnost / uncertainty:** Several East and South traditions commonly use a masculine method head. ## OLISV-T0178 · logic.axiomatization - **English lemma / sense:** axiomatization; axiomatized by — Presentation of a theory as the semantic-consequence closure of a selected set of axioms. - **Medžuslovjansky:** `aksiomatizacija`; lemma `aksiomatizacija`; feminine noun. - **Upotrěbljenje / inflection:** Decline as a regular feminine -acija noun; the passive verbal surface is aksiomatizovany, with neuter aksiomatizovano for množstvo. - **Kirilična forma:** `аксиоматизација` - **Argumentacija / rationale:** Aksiomatizacija is directly listed, pan-Slavically transparent, and exactly names the operation described by the source. The translation uses the agreeing passive aksiomatizovano where the grammatical head is neuter množstvo. - **Uvěrjenost / status:** 0.96 (high); `provisional`; revision `OLISV-T0178-r0001`. - **Slovjanske sravnenja / comparanda:** ru: аксиоматизация; uk: аксіоматизація; pl: aksjomatyzacja; cs: axiomatizace; bcs: aksiomatizacija; bg: аксиоматизация. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[1501]; dictionary_id=37794; lemma=aksiomatizacija; gloss=axiomatization); ISV-DICT-LIVE-20260825 (wordList[1498-1500]; dictionary_id=24180,37533,37534; lemma=aksioma,aksiomatičny,aksiomatika); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** aksiomovanje: A native-looking deverbal noun is possible, but the frozen dictionary directly supplies aksiomatizacija across all comparison columns and therefore gives the stronger reproducible choice. - **Neizvěstnost / uncertainty:** The dictionary attests the noun, while the exact agreeing passive surface in prose is a regular derivation rather than a separate listed headword. ## OLISV-T0284 · logic.bhk-interpretation - **English lemma / sense:** BHK interpretation — The Brouwer-Heyting-Kolmogorov proof interpretation of intuitionistic connectives and quantifiers. - **Medžuslovjansky:** `interpretacija BHK`; lemma `interpretacija BHK`; feminine noun plus acronym. - **Upotrěbljenje / inflection:** Feminine interpretacija; genitive interpretacije BHK. Keep the acronym invariant. - **Kirilična forma:** `интерпретација БХК` - **Argumentacija / rationale:** Interpretacija BHK uses the direct interpretation head and leaves the internationally recognized acronym visible, while the source supplies the complete proof-theoretic clauses. - **Uvěrjenost / status:** 0.97 (high); `provisional`; revision `OLISV-T0284-r0001`. - **Slovjanske sravnenja / comparanda:** ru: интерпретация БГК; uk: інтерпретація БГК; pl: interpretacja BHK; cs: BHK interpretace; bcs: BHK interpretacija; БХК интерпретација; bg: БХК интерпретация. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 97-112); ISV-DICT-LIVE-20260825 (dictionary_id=4988; lemma=interpretacija; gloss=interpretation); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** interpretacija Brouwera, Heytinga i Kolmogorova: The expanded form is accurate but unwieldy as the recurring canonical head; the names remain in the definition. - **Neizvěstnost / uncertainty:** National acronym ordering and scripts vary; the Latin BHK label follows the source and remains searchable. ## OLISV-T0116 · logic.biconditional - **English lemma / sense:** biconditional — The binary connective true exactly when its two component formulas have the same truth value. - **Medžuslovjansky:** `dvojsměrna implikacija`; lemma `dvojsměrna implikacija`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive dvojsměrnoj implikacije; materialna ekvivalentnost is a semantic synonym in this setting. - **Kirilična forma:** `двојсмєрна импликација` - **Argumentacija / rationale:** The descriptive phrase is more broadly transparent than the compressed international loan. - **Uvěrjenost / status:** 0.7 (medium); `provisional`; revision `OLISV-T0116-r0001`. - **Slovjanske sravnenja / comparanda:** ru: эквиваленция; бикондиционал; uk: еквіваленція; бікондиціонал; pl: równoważność; bikondycjonał; cs: ekvivalence; bikondicionál; bcs: ekvivalencija; еквиваленција; bg: еквиваленция. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** bikondicional: The loan is concise but is unevenly established and opaque to readers without English-derived terminology. - **Neizvěstnost / uncertainty:** Several traditions prefer equivalence rather than biconditional terminology. ## OLISV-T0154 · logic.bound-variable-occurrence - **English lemma / sense:** bound occurrence of a variable — An occurrence of a variable in a formula that lies in the scope of a corresponding quantifier occurrence and is bound by it; the status is relative to the containing formula. - **Medžuslovjansky:** `svezano pojavjenje prěměnnoj`; lemma `svezano pojavjenje prěměnnoj`; neuter noun phrase. - **Upotrěbljenje / inflection:** Genitive svezanogo pojavjenja prěměnnoj. The etymological TeX reader displays svęzano pojavjenje; svęzana prěměnna is only contextual shorthand. - **Kirilična forma:** `свезано појавјење прємєнној` - **Argumentacija / rationale:** The positive bound/free pair follows the accepted OLP-0144 wording and keeps the formal object at occurrence level. The standard-Latin machine head svezano normalizes the directly listed svęzany component; etymological display remains explicit in the use note and continuous reader. - **Uvěrjenost / status:** 0.82 (medium); `provisional`; revision `OLISV-T0154-r0001`. - **Slovjanske sravnenja / comparanda:** ru: связанное вхождение переменной; uk: пов'язане входження змінної; pl: związane wystąpienie zmiennej; cs: vázaný výskyt proměnné; bcs: vezana pojava varijable; везана појава променљиве; bg: свързано срещане на променлива. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-DICT-LIVE-20260825 (wordList[4013]; dictionary_id=3512); ISV-DICT-LIVE-20260825 (wordList[965]; dictionary_id=10818); ISV-DICT-LIVE-20260825 (wordList[18234]; dictionary_id=35526); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** nesvezano pojavjenje prěměnnoj: Unbound is useful pedagogical paraphrase but defines the free side negatively and does not name the source's positive bound category.; obvezano pojavjenje prěměnnoj: Obvezano risks the obligatory or mandatory sense and is not the accepted edition binding verb family. - **Neizvěstnost / uncertainty:** The dictionary adjective has the broader connected/related sense; Open Logic supplies the variable-binding restriction.; Standard-Latin svezano and etymological-display svęzano are two scripted surfaces of one edition head, not competing concepts.; No native or official certification is claimed for the complete specialist compound. ## OLISV-T0307 · logic.box-operator - **English lemma / sense:** box operator — The modal operator Box, written □, asserting that its argument is necessarily true. - **Medžuslovjansky:** `operator neobhodnosti`; lemma `operator neobhodnosti`; masculine noun phrase. - **Upotrěbljenje / inflection:** Masculine operator; genitive operatora neobhodnosti. The symbol is written $\Box$. - **Kirilična forma:** `оператор необходности` - **Argumentacija / rationale:** Operator neobhodnosti names the symbol by its semantic function rather than its typographic shape, while the source explicitly introduces Box and its necessary-truth reading. This avoids a reader having to infer what 'square' means. - **Uvěrjenost / status:** 0.88 (high); `provisional`; revision `OLISV-T0307-r0001`. - **Slovjanske sravnenja / comparanda:** ru: оператор необходимости (□); uk: оператор необхідності (□); pl: operator konieczności (□); cs: operátor nutnosti (□); bcs: operator nužnosti (□); bg: оператор за необходимост (□). - **Dokazy / evidence:** OL-FOL-BEYOND-MODAL-LOGICS (lines 31-38); ISV-DICT-LIVE-20260825 (dictionary_id=33109; lemma=neobhodimosť; gloss=necessity); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** operator kvadrata: A literal typographic calque is understandable but hides the operator's logical role and can be confused with a square-operation symbol. - **Neizvěstnost / uncertainty:** National texts may call the symbol box, square, or necessity operator; the canon records the semantic choice and preserves the source notation. ## OLISV-T0327 · logic.causal - **English lemma / sense:** causal logic — A logic designed in the source to model reasoning about causal relationships. - **Medžuslovjansky:** `pričinna logika`; lemma `pričinna logika`; feminine adjective-noun phrase. - **Upotrěbljenje / inflection:** Feminine logika; genitive pričinnoj logiky and plural pričinne logiky. - **Kirilična forma:** `причинна логика` - **Argumentacija / rationale:** Pričinna logika combines two direct frozen lemmas and exposes the shared cause root more transparently than the international kauzal- loan. The source limits the compound to a family of logics about causal relationships. - **Uvěrjenost / status:** 0.93 (high); `provisional`; revision `OLISV-T0327-r0001`. - **Slovjanske sravnenja / comparanda:** ru: причинная логика; каузальная логика; uk: причинна логіка; каузальна логіка; pl: logika przyczynowa; logika kauzalna; cs: příčinná logika; kauzální logika; bcs: uzročna logika; каузална логика; bg: причинна логика. - **Dokazy / evidence:** OL-FOL-BEYOND-OTHER-LOGICS (lines 29-30); ISV-DICT-LIVE-20260825 (dictionary_id=37297; lemma=pričinny; gloss=causal); ISV-DICT-LIVE-20260825 (dictionary_id=8933; lemma=logika; gloss=logic); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** kauzalna logika: The international loan is specialist-searchable, but the directly attested pričinny family is more immediately accessible across the intended non-English readership. - **Neizvěstnost / uncertainty:** Some specialist traditions prefer the kauzal- internationalism; it remains recorded as a comparandum rather than the preferred head. ## OLISV-T0328 · logic.causal-relationship - **English lemma / sense:** causal relationship — A relationship in which one event, condition, or state functions causally with respect to another, as modeled by causal logic in the source. - **Medžuslovjansky:** `pričinna svęź`; lemma `pričinna svęź`; feminine adjective-noun phrase. - **Upotrěbljenje / inflection:** Feminine use of svęź in this compound; locative plural pričinnyh svęzah. - **Kirilična forma:** `причинна свез` - **Argumentacija / rationale:** Pričinna svęź directly composes the frozen causal and relationship lemmas and yields a broadly recognizable phrase. It names a relation, not merely the everyday fact that two things are associated. - **Uvěrjenost / status:** 0.92 (high); `provisional`; revision `OLISV-T0328-r0001`. - **Slovjanske sravnenja / comparanda:** ru: причинная связь; uk: причинний зв'язок; pl: związek przyczynowy; cs: příčinná souvislost; bcs: uzročna veza; узрочна веза; bg: причинна връзка. - **Dokazy / evidence:** OL-FOL-BEYOND-OTHER-LOGICS (lines 29-30); ISV-DICT-LIVE-20260825 (dictionary_id=37297; lemma=pričinny; gloss=causal); ISV-DICT-LIVE-20260825 (dictionary_id=18741; lemma=svęź; gloss=connection, relationship, bond); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** pričinno odnošenje: Odnošenje is viable for a formally defined binary relation, but the source uses the broader ordinary-language relationship sense, for which svęź is more transparent. - **Neizvěstnost / uncertainty:** Svęź is listed with variable gender; the edition fixes feminine agreement in this occurrence without claiming universal grammatical exclusivity. ## OLISV-T0270 · logic.classical - **English lemma / sense:** classical logic — The classical logical framework contrasted with intuitionistic restrictions in proof principles, semantics, and double-negation translation. - **Medžuslovjansky:** `klasična logika`; lemma `klasična logika`; feminine noun phrase. - **Upotrěbljenje / inflection:** Feminine logika; genitive klasičnoj logikě. Use klasična consistently with the target and the dictionary adjective row. - **Kirilična forma:** `класична логика` - **Argumentacija / rationale:** Klasična logika is directly compositional and names the contrast made in the final paragraph. The canon keeps it parallel to T0269, so readers can track the constructive/classical opposition without an invented synonym. The dedicated OLP-0179 unit now broadens the current sense while the earlier revision remains preserved as scope provenance. - **Uvěrjenost / status:** 0.97 (high); `provisional`; revision `OLISV-T0270-r0003`. - **Slovjanske sravnenja / comparanda:** ru: классическая логика; uk: класична логіка; pl: logika klasyczna; cs: klasická logika; bcs: klasična logika; класична логика; bg: класическа логика. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 13-15, 32-35, 114-178, and 186-198); OL-FOL-BEYOND-HIGHER-ORDER-LOGIC (lines 118-123); ISV-DICT-LIVE-20260825 (dictionary_id=8459; lemma=klasičny; gloss=classical, classic); ISV-DICT-LIVE-20260825 (dictionary_id=8933; lemma=logika; gloss=logic); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** tradicionna logika: Traditional is sociological and does not identify the formal classical system.; neintuicionistična logika: A negative description is less readable and fails to preserve the source's conventional label. - **Neizvěstnost / uncertainty:** The adjective is polysemous in general language; the source context fixes the formal sense.; The r0001 record is preserved as adverse provenance for the evidence correction.; Earlier narrower sense wording remains preserved in the superseded revision. ## OLISV-T0130 · logic.closed-term - **English lemma / sense:** closed term — A first-order term containing no variable occurrence. - **Medžuslovjansky:** `zamknuty term`; lemma `zamknuty term`; masculine noun phrase. - **Upotrěbljenje / inflection:** Genitive zamknutogo terma; use only for the syntactic no-free-variable sense. - **Kirilična forma:** `замкнуты терм` - **Argumentacija / rationale:** The direct closed adjective bridges Russian, Ukrainian, Polish and Czech forms and is already stable throughout the edition's completeness tranche. - **Uvěrjenost / status:** 0.82 (medium); `provisional`; revision `OLISV-T0130-r0001`. - **Slovjanske sravnenja / comparanda:** ru: замкнутый терм; uk: замкнений терм; pl: term zamknięty; cs: uzavřený term; bcs: zatvoreni term; затворени терм; bg: затворен терм. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[3510]; dictionary_id=31523); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** zatvorjeny term: This strong South-Slavic and Czech-facing variant remains common in earlier proof-system units but is not selected as the single canon head. - **Neizvěstnost / uncertainty:** Earlier accepted units alternate zamknuty and zatvorjeny; the later normalization must remain monotonic and reversible. ## OLISV-T0137 · logic.closing-parenthesis - **English lemma / sense:** closing parenthesis — The right member of a parenthesis pair that ends a grouped expression. - **Medžuslovjansky:** `zatvarjajuća zatvorka`; lemma `zatvarjajuća zatvorka`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive zatvarjajućej zatvorky; pair with otvarjajuća zatvorka. - **Kirilična forma:** `затварјајуча затворка` - **Argumentacija / rationale:** Direct close and parenthesis components yield a transparent form matching every comparison language's directional distinction. - **Uvěrjenost / status:** 0.9 (high); `provisional`; revision `OLISV-T0137-r0001`. - **Slovjanske sravnenja / comparanda:** ru: закрывающая скобка; uk: закривна дужка; pl: nawias zamykający; cs: uzavírací závorka; bcs: zatvarajuća zagrada; затварајућа заграда; bg: затваряща скоба. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[3508]; dictionary_id=5204); ISV-DICT-LIVE-20260825 (wordList[2433]; dictionary_id=35498); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** prava zatvorka: Right is visually clear but less robust across writing-direction contexts and does not name the closing function. - **Neizvěstnost / uncertainty:** The participial compound is compositional rather than a direct row. ## OLISV-T0062 · logic.compactness - **English lemma / sense:** compactness — The property that satisfiability of every finite subset guarantees satisfiability of the entire set. - **Medžuslovjansky:** `kompaktnost`; lemma `kompaktnost`; feminine noun. - **Upotrěbljenje / inflection:** Feminine abstract noun derived from kompaktny; use teorema kompaktnosti for the theorem. - **Kirilična forma:** `компактност` - **Argumentacija / rationale:** Kompaktnost preserves the internationally shared compact- root used across most Slavic mathematical traditions and forms a transparent abstract noun; the surrounding definition supplies the non-spatial logical sense, while the Polish divergence is recorded rather than concealed. - **Uvěrjenost / status:** 0.69 (medium); `provisional`; revision `OLISV-T0062-r0001`. - **Slovjanske sravnenja / comparanda:** ru: компактность; uk: компактність; pl: zwartość; cs: kompaktnost; bcs: kompaktnost; bg: компактност. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[3759]; dictionary_id=33088); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** zgustjenost: A native density-style calque suggests physical packing or topological density and does not identify the finite-subset property stated by Open Logic. - **Neizvěstnost / uncertainty:** The exact abstract noun and specialist logical sense are editorial derivations from a directly attested component, and Polish mathematical usage does not share the selected stem. ## OLISV-T0061 · logic.completeness - **English lemma / sense:** completeness — The property that every semantic consequence is derivable in the selected proof system. - **Medžuslovjansky:** `polnota`; lemma `polnota`; feminine noun. - **Upotrěbljenje / inflection:** Feminine abstract noun; use polny for the corresponding adjective and teorema polnoty for the theorem. - **Kirilična forma:** `полнота` - **Argumentacija / rationale:** Polnota keeps the full/whole semantic core visible to readers across East, West, and South Slavic traditions and has already remained stable throughout the accepted completeness block; it is less morphologically marked than dictionary popȯlnosť and less dependent on an international loan than kompletnost. - **Uvěrjenost / status:** 0.72 (medium); `provisional`; revision `OLISV-T0061-r0001`. - **Slovjanske sravnenja / comparanda:** ru: полнота, завершённость; uk: повнота, завершеність; pl: zupełność, kompletność; cs: úplnost, kompletnost; bcs: potpunost; bg: пълнота. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[3821-3822]; dictionary_id=4378,10922); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** popȯlnosť: This is a direct dictionary completeness lemma, but its etymological vowel and suffix make the running theorem phrase less immediately transparent than the established edition form.; kompletnost: The international stem is broadly recognizable but is less transparent to readers who rely on the native full/whole family and would break accepted edition continuity. - **Neizvěstnost / uncertainty:** The selected surface polnota is not itself a lemma in the pinned dictionary response; it is an edition-level normalization supported by the national comparanda and continuous translated usage. ## OLISV-T0238 · logic.comprehension-schema - **English lemma / sense:** comprehension schema — The second-order axiom schema asserting a relation for each formula that defines its extension, with the relation variable not free in that formula. - **Medžuslovjansky:** `shema tvorjenja`; lemma `shema tvorjenja`; feminine noun phrase. - **Upotrěbljenje / inflection:** Nominative shema tvorjenja; genitive shemy tvorjenja. Keep tvorjenje distinct from a generic formation rule. - **Kirilična forma:** `схема творјења` - **Argumentacija / rationale:** The source explicitly names a schema and distinguishes it from the broader derivation rules. Shema is a direct dictionary lemma; tvorjenje is a transparent productive nominalization and is kept separate from the existing naive set-comprehension entry. - **Uvěrjenost / status:** 0.82 (high); `provisional`; revision `OLISV-T0238-r0002`. - **Slovjanske sravnenja / comparanda:** ru: схема образования; uk: схема утворення; pl: schemat tworzenia; cs: schéma tvorby; bcs: shema tvorjenja; схема творења; bg: схема на образуване. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (dictionary_id=18814; lemma=shema; gloss=scheme); ISV-DICT-LIVE-20260825 (dictionary_id=3030; lemma=tvoriti; gloss=create, form); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** naivna shema tvorjenja: Already reserved for naive set comprehension and would erase the second-order distinction.; pravilo tvorjenja: Names a rule rather than the axiom schema itself. - **Neizvěstnost / uncertainty:** No direct dictionary headword for the specialist phrase; the existing canon distinguishes the set-theoretic naive schema.; The r0001 record remains preserved as adverse provenance for the target/source locator mismatch. ## OLISV-T0134 · logic.concatenation - **English lemma / sense:** concatenation — The operation that joins symbol strings in order without changing their internal token order. - **Medžuslovjansky:** `konkatenacija`; lemma `konkatenacija`; feminine noun. - **Upotrěbljenje / inflection:** Genitive konkatenacije; arguments are ordered symbol strings. - **Kirilična forma:** `конкатенација` - **Argumentacija / rationale:** The international specialist form is nearly identical across all comparison traditions and avoids an improvised native metaphor. - **Uvěrjenost / status:** 0.9 (high); `provisional`; revision `OLISV-T0134-r0001`. - **Slovjanske sravnenja / comparanda:** ru: конкатенация; uk: конкатенація; pl: konkatenacja; cs: konkatenace; bcs: konkatenacija; конкатенација; bg: конкатенация. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** sojedinjenje nizov: The descriptive alternative is understandable but can denote set-like or unordered joining rather than ordered string concatenation. - **Neizvěstnost / uncertainty:** No exact frozen dictionary row attests the computational noun. ## OLISV-T0115 · logic.conditional - **English lemma / sense:** conditional — The binary material conditional connective, false only when its antecedent is true and consequent false. - **Medžuslovjansky:** `uslovny sveznik`; lemma `uslovny sveznik`; masculine noun phrase. - **Upotrěbljenje / inflection:** Genitive uslovnogo sveznika; use implikacija for the corresponding formula or relation where context permits. - **Kirilična forma:** `условны свезник` - **Argumentacija / rationale:** Native uslovny is directly attested and the connective head preserves the symbol category. - **Uvěrjenost / status:** 0.72 (medium); `provisional`; revision `OLISV-T0115-r0001`. - **Slovjanske sravnenja / comparanda:** ru: условная связка; uk: умовний сполучник; pl: implikacja materialna; cs: materiální implikace; bcs: uslovni veznik; условни везник; bg: условна връзка. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[3931]; dictionary_id=1618); ISV-DICT-LIVE-20260825 (wordList[4001]; dictionary_id=36359); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** kondicional: The direct dictionary noun is grammatical rather than logic-specific and is less transparent outside South Slavic. - **Neizvěstnost / uncertainty:** The source glossary key remains conditional and may render a different surface until glossary localization is frozen. ## OLISV-T0301 · logic.conditional-assertion - **English lemma / sense:** conditional assertion — A claim expressed with an antecedent and consequent, whose material truth may suggest a stronger counterfactual connection. - **Medžuslovjansky:** `uslovno tvrdženje`; lemma `uslovno tvrdženje`; neuter adjective-verbal-noun phrase. - **Upotrěbljenje / inflection:** Neuter tvrdženje; genitive uslovnogo tvrdženja. - **Kirilična forma:** `условно тврджење` - **Argumentacija / rationale:** Uslovno tvrdženje uses the direct conditional component and the edition's established truth-apt tvrdženje head. It preserves the source's warning that material truth alone can mislead without collapsing the claim into a strict counterfactual term. - **Uvěrjenost / status:** 0.9 (high); `provisional`; revision `OLISV-T0301-r0001`. - **Slovjanske sravnenja / comparanda:** ru: условное утверждение; uk: умовне твердження; pl: twierdzenie warunkowe; cs: podmíněné tvrzení; bcs: uslovna tvrdnja; условна тврдња; bg: условно твърдение. - **Dokazy / evidence:** OL-FOL-BEYOND-MODAL-LOGICS (lines 13-29); ISV-DICT-LIVE-20260825 (dictionary_id=1618; lemma=uslovny; gloss=conditional); ISV-DICT-LIVE-20260825 (dictionary_id=1087; lemma=tvŕđeńje; gloss=statement, claim, assertion); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** uslovno izrečenje: The general utterance noun is intelligible, but tvrdženje is already the edition's truth-apt statement head and better preserves the logical force. - **Neizvěstnost / uncertainty:** National traditions distinguish conditional sentence, proposition, and assertion in different ways; the source's explanatory paragraph fixes the intended scope. ## OLISV-T0109 · logic.conjunction - **English lemma / sense:** conjunction — The conjunction connective, classically truth-functional and constructively interpreted as requiring a paired proof of both conjuncts. - **Medžuslovjansky:** `konjunkcija`; lemma `konjunkcija`; feminine noun. - **Upotrěbljenje / inflection:** Genitive konjunkcije; reserve svęznik for the superordinate connective category. - **Kirilična forma:** `конјункција` - **Argumentacija / rationale:** Direct dictionary logic sense and near-unanimous international comparison support. The dedicated OLP-0179 unit now broadens the current sense while the earlier revision remains preserved as scope provenance. - **Uvěrjenost / status:** 0.94 (high); `provisional`; revision `OLISV-T0109-r0002`. - **Slovjanske sravnenja / comparanda:** ru: конъюнкция; uk: кон'юнкція; pl: koniunkcja; cs: konjunkce; bcs: konjukcija; конјункција; bg: конюнкция. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 97-107 and 215); ISV-DICT-LIVE-20260825 (wordList[4002]; dictionary_id=808); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** logično i: The descriptive reading is useful pedagogically but is not a stable compact terminological head. - **Neizvěstnost / uncertainty:** Croatian spelling in the frozen row omits one n; the canonical international form follows the Interslavic lemma.; Earlier narrower sense wording remains preserved in the superseded revision. ## OLISV-T0303 · logic.consequent - **English lemma / sense:** consequent — The conclusion or second component of a conditional assertion, written B in the source's material and modal discussion. - **Medžuslovjansky:** `poslědica`; lemma `poslědica`; feminine noun. - **Upotrěbljenje / inflection:** Feminine poslědica; genitive poslědice and instrumental poslědicoju. - **Kirilična forma:** `послєдица` - **Argumentacija / rationale:** Poslědica is a directly listed consequence noun and makes the conclusion sense readable without importing an opaque Latinism. The source's conditional and modal passages narrow the broad everyday consequence field to the consequent position. - **Uvěrjenost / status:** 0.86 (high); `provisional`; revision `OLISV-T0303-r0001`. - **Slovjanske sravnenja / comparanda:** ru: консеквент; следствие; uk: консеквент; наслідок; pl: następnik; konsekwent; cs: konsekvent; důsledek; bcs: konsekvent; posljedica; bg: консеквент; следствие. - **Dokazy / evidence:** OL-FOL-BEYOND-MODAL-LOGICS (lines 20-25); ISV-DICT-LIVE-20260825 (dictionary_id=18328; lemma=poslědica; gloss=consequence, result, outcome); ISV-DICT-LIVE-20260825 (dictionary_id=2327; lemma=poslědstvo; gloss=consequence, result, effect); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** konsekvent: The international technical form is familiar to specialists, but the directly attested consequence noun is more transparent across the target readership. - **Neizvěstnost / uncertainty:** Some national logic texts reserve a konsekvent-type loan for the formal term; the edition retains that comparandum while preferring the transparent head. ## OLISV-T0098 · logic.constant-symbol - **English lemma / sense:** constant symbol — A zero-argument nonlogical symbol naming an individual object in a first-order structure. - **Medžuslovjansky:** `konstantny simbol`; lemma `konstantny simbol`; masculine noun phrase. - **Upotrěbljenje / inflection:** Genitive konstantnogo simbola; use konstanta only as context permits, never for the interpreted object itself. - **Kirilična forma:** `константны симбол` - **Argumentacija / rationale:** The explicit symbol head prevents the source's pedagogical shorthand from conflating syntax with interpretation. - **Uvěrjenost / status:** 0.69 (medium); `provisional`; revision `OLISV-T0098-r0001`. - **Slovjanske sravnenja / comparanda:** ru: константный символ; uk: константний символ; pl: symbol stałej; cs: symbol konstanty; bcs: konstantni simbol; константни симбол; bg: константен символ. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[16812]; dictionary_id=12221); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** konstanta: The bare noun can conflate the object-language symbol, its interpretation, and an ordinary mathematical constant. - **Neizvěstnost / uncertainty:** No exact frozen dictionary row attests the complete specialist compound. ## OLISV-T0271 · logic.constructive-semantics - **English lemma / sense:** constructive semantics — A semantics whose type interpretations are developed constructively rather than by the classical alternative. - **Medžuslovjansky:** `konstruktivna semantika`; lemma `konstruktivna semantika`; feminine noun phrase. - **Upotrěbljenje / inflection:** Feminine semantika; genitive konstruktivnoj semantiky. Use konstruktivna for the adjective and keep the semantic head. - **Kirilična forma:** `конструктивна семантика` - **Argumentacija / rationale:** Konstruktivna semantika follows the source's repeated constructive terminology and makes the interpretation regime explicit. The direct semantika noun and konstrukcija root support the compositional derivation; the phrase is not collapsed into intuitionistic logic. - **Uvěrjenost / status:** 0.86 (high); `provisional`; revision `OLISV-T0271-r0002`. - **Slovjanske sravnenja / comparanda:** ru: конструктивная семантика; uk: конструктивна семантика; pl: semantyka konstruktywna; cs: konstruktivní sémantika; bcs: konstruktivna semantika; конструктивна семантика; bg: конструктивна семантика. - **Dokazy / evidence:** OL-FOL-BEYOND-HIGHER-ORDER-LOGIC (lines 114-123); ISV-DICT-LIVE-20260825 (dictionary_id=4873; lemma=konstrukcija; gloss=construction); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3); ISV-DICT-LIVE-20260825 (dictionary_id=35935; lemma=semantika; gloss=semantics) - **Alternativy / alternatives:** semantika intuicionističnoj logiki: Too narrow: the source describes constructive versions and their interpretations, not only one logic label.; izgradžajuća semantika: A literal building metaphor is less recognizable and unsupported as a specialist head. - **Neizvěstnost / uncertainty:** The full specialist compound is compositional; national literature varies between constructive and intuitionistic as overlapping but non-identical qualifiers.; The r0001 record is preserved as adverse provenance for the evidence correction. ## OLISV-T0089 · logic.contradiction - **English lemma / sense:** contradiction — A formula or pair of claims that cannot be true together, exemplified by A and not-A. - **Medžuslovjansky:** `protivrěčnost`; lemma `protivrěčnost`; feminine noun. - **Upotrěbljenje / inflection:** Genitive singular protivrěčnosti; use protivrěčny for contradictory and keep consistency as a separately adjudicated sense. - **Kirilična forma:** `противрєчност` - **Argumentacija / rationale:** The direct dictionary noun maps the core contradiction families across all comparison traditions; the formula context excludes ordinary disagreement. - **Uvěrjenost / status:** 0.81 (high); `provisional`; revision `OLISV-T0089-r0001`. - **Slovjanske sravnenja / comparanda:** ru: противоречие; противоречивость; uk: суперечність; pl: sprzeczność; cs: protiřečení; rozpor; bcs: proturječnost; protivr(e)čnost; bg: противоречие. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[9113]; dictionary_id=23802); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** protivnost: This denotes contrary, opposition, or contradistinction rather than a formal contradiction.; kontradikcija: The international loan is less transparent and not directly listed. - **Neizvěstnost / uncertainty:** The existing consistency entry uses nesprotivnost rather than morphologically tighter neprotivrěčnost; the tension is recorded rather than silently erased. ## OLISV-T0378 · logic.converse-proposition - **English lemma / sense:** converse proposition — For a proposition of the form p implies q, the proposition with antecedent and consequent exchanged, q implies p; it is distinct from the inverse and contrapositive and need not share the original's truth. - **Medžuslovjansky:** `obratno tvrdženje`; lemma `obratno tvrdženje`; neuter adjective-noun phrase. - **Upotrěbljenje / inflection:** Neuter nominative obratno tvrdženje; genitive obratnogo tvrdženja. Use the complement k with dative when naming the original proposition. - **Kirilična forma:** `обратно тврджење` - **Argumentacija / rationale:** Obratno tvrdženje composes two official Interslavic heads and follows the South-Slavic obrat- family. The Polish witness supplies the decisive semantic taxonomy, while Ukrainian and Slovenian independently attest converse-statement or converse-implication usage. The canon definition explicitly prevents collision with inverse and contrapositive. - **Uvěrjenost / status:** 0.91 (high); `provisional`; revision `OLISV-T0378-r0001`. - **Slovjanske sravnenja / comparanda:** ru: обратное утверждение; uk: обернене твердження; pl: twierdzenie odwrotne; cs: obrácené tvrzení; bcs: obratna tvrdnja; обратна тврдња; bg: обратно твърдение. - **Dokazy / evidence:** OL-MODEL-ARITHMETIC-STANDARD-MODELS (lines 52-57); ISV-DICT-LIVE-20260825 (wordList[14417]; dictionary_id=18030; lemma=obråtny; gloss=reverse); ISV-DICT-LIVE-20260825 (wordList[16219]; dictionary_id=1087; lemma=tvŕđeńje; gloss=statement, claim, assertion); UK-KNU-MODEL-THEORY-2023 (physical page 19 / decoded extract line 898; physical page 61 / line 3192); PL-AMU-MATHEMATICAL-METHODS-CONVERSE (physical page 2 / extracted lines 51-65); SL-LJUBLJANA-ALGEBRA-DISCRETE-MATH-2011 (printed page 21 / physical page 27 / extracted lines 898-905); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic, standard flavorization) - **Alternativy / alternatives:** protivno tvrdženje: This risks the inverse or contrary proposition, which the Polish source distinguishes from the converse.; protivopoložno tvrdženje: Opposite is semantically broader and does not encode exchange of antecedent and consequent.; obratna implikacija: Directly supported in Slovenian and suitable when the object is explicitly an implication; the source asks for the converse proposition, so tvrdženje preserves the source category. - **Neizvěstnost / uncertainty:** The selected full phrase is compositional rather than a standalone dictionary headword.; Direct sources vary between proposition/statement and implication heads; this entry is restricted to the proposition sense used by OLP-0193. ## OLISV-T0285 · logic.curry-howard-isomorphism - **English lemma / sense:** Curry-Howard isomorphism — The correspondence in which formulas are treated as types and proofs as computational objects inhabiting those types. - **Medžuslovjansky:** `izomorfizm Kurrija--Hauarda`; lemma `izomorfizm Kurrija--Hauarda`; masculine noun with coordinated proper-name genitives. - **Upotrěbljenje / inflection:** Masculine izomorfizm; genitive izomorfizma Kurrija--Hauarda. Preserve both adapted names and the double-name dash. - **Kirilična forma:** `изоморфизм Куррија--Хауарда` - **Argumentacija / rationale:** The international named head preserves the literature's searchable label, while the source's formulas/types/proofs explanation fixes the specific correspondence rather than an arbitrary structural isomorphism. - **Uvěrjenost / status:** 0.89 (high); `provisional`; revision `OLISV-T0285-r0001`. - **Slovjanske sravnenja / comparanda:** ru: изоморфизм Карри—Ховарда; uk: ізоморфізм Каррі—Говарда; pl: izomorfizm Curry'ego-Howarda; cs: Curryho-Howardův izomorfismus; bcs: Curry-Howardov izomorfizam; Кари—Хауардов изоморфизам; bg: изоморфизъм на Къри—Хауърд. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 108-112); ISV-DICT-LIVE-20260825 (dictionary_id=5181; lemma=formula; gloss=formula); ISV-DICT-LIVE-20260825 (dictionary_id=3224; lemma=tip; gloss=type, kind); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** sootvětnost formul i tipov: A descriptive correspondence phrase loses the conventional proper name and the source's isomorphism claim. - **Neizvěstnost / uncertainty:** No direct dictionary isomorphism head is available; the proper-name inflection and technical noun are edition-level choices. ## OLISV-T0290 · logic.deductive-equivalence - **English lemma / sense:** deductive equivalence — Mutual derivability of principles within the stated deductive system. - **Medžuslovjansky:** `deduktivna ekvivalentnost`; lemma `deduktivna ekvivalentnost`; feminine adjective-derived-noun phrase. - **Upotrěbljenje / inflection:** Feminine ekvivalentnost; genitive deduktivnoj ekvivalentnosti. - **Kirilična forma:** `дедуктивна еквивалентност` - **Argumentacija / rationale:** The noun phrase transparently derives from two direct adjectives and fixes equivalence as mutual derivability rather than semantic sameness. - **Uvěrjenost / status:** 0.93 (high); `provisional`; revision `OLISV-T0290-r0001`. - **Slovjanske sravnenja / comparanda:** ru: дедуктивная эквивалентность; uk: дедуктивна еквівалентність; pl: równoważność dedukcyjna; cs: deduktivní ekvivalence; bcs: deduktivna ekvivalentnost; дедуктивна еквивалентност; bg: дедуктивна еквивалентност. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 117-126); ISV-DICT-LIVE-20260825 (dictionary_id=25163; lemma=deduktivny; gloss=deductive); ISV-DICT-LIVE-20260825 (dictionary_id=36133; lemma=ekvivalentny; gloss=equivalent, tantamount); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** logična ekvivalentnost: Logical equivalence can mean equal truth conditions; the source specifically asserts deductive interderivability. - **Neizvěstnost / uncertainty:** Ekvivalentnost is a regular derivative rather than a direct dictionary noun row. ## OLISV-T0322 · logic.default - **English lemma / sense:** default logic — A nonclassical logic that licenses normally applicable assumptions or rules whose conclusions may be withdrawn when new information arrives. - **Medžuslovjansky:** `defaultna logika`; lemma `defaultna logika`; feminine adjective-noun phrase. - **Upotrěbljenje / inflection:** Feminine logika; genitive defaultnoj logiky and plural defaultne logiky. At first use, append the explanatory alias logika odzyvatelnyh prědpokladov. - **Kirilična forma:** `дефаултна логика` - **Argumentacija / rationale:** Defaultna logika preserves the internationally searchable specialist label, while the running-text alias logika odzyvatelnyh prědpokladov makes its defeasible function legible without English. The source's later-withdrawal explanation prevents the alias from being read as an ordinary fixed assumption. - **Uvěrjenost / status:** 0.72 (medium); `provisional`; revision `OLISV-T0322-r0001`. - **Slovjanske sravnenja / comparanda:** ru: логика по умолчанию; uk: логіка за замовчуванням; pl: logika domyślna; cs: defaultní logika; bcs: logika po pretpostavci; логика по подразумевању; bg: логика по подразбиране. - **Dokazy / evidence:** OL-FOL-BEYOND-OTHER-LOGICS (lines 25-28); ISV-DICT-LIVE-20260825 (dictionary_id=36575; lemma=prědustavjeńje; gloss=preset, default setting); ISV-DICT-LIVE-20260825 (dictionary_id=5324; lemma=prědpoklad; gloss=assumption); ISV-DICT-LIVE-20260825 (dictionary_id=8933; lemma=logika; gloss=logic); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** logika po umolčanju: This East-Slavic-style calque is unevenly transparent elsewhere and can be read as a software setting rather than a defeasible logical formalism. - **Neizvěstnost / uncertainty:** The full specialist loan is not directly listed in the frozen dictionary, and the dictionary's default-setting noun is adverse rather than sufficient evidence. ## OLISV-T0107 · logic.defined-symbol - **English lemma / sense:** defined symbol — A notational symbol introduced as an abbreviation for expressions in the primitive vocabulary. - **Medžuslovjansky:** `definovany simbol`; lemma `definovany simbol`; masculine noun phrase. - **Upotrěbljenje / inflection:** Genitive definovanogo simbola; the definition must expand back into the primitive language. - **Kirilična forma:** `дефинованы симбол` - **Argumentacija / rationale:** Definovany is already used consistently in the edition and the symbol head is directly attested. - **Uvěrjenost / status:** 0.79 (medium); `provisional`; revision `OLISV-T0107-r0001`. - **Slovjanske sravnenja / comparanda:** ru: определённый символ; uk: визначений символ; pl: symbol zdefiniowany; cs: definovaný symbol; bcs: definirani simbol; дефинисани симбол; bg: дефиниран символ. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[4862]; dictionary_id=2624); ISV-DICT-LIVE-20260825 (wordList[16812]; dictionary_id=12221); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** opreděljeny simbol: The alternative is grammatical but can mean merely determined rather than explicitly introduced by definition. - **Neizvěstnost / uncertainty:** The exact participial compound is editorial rather than a direct dictionary lemma. ## OLISV-T0329 · logic.deontic - **English lemma / sense:** deontic logic — A logic designed in the source to model reasoning about moral and ethical obligations. - **Medžuslovjansky:** `deontična logika`; lemma `deontična logika`; feminine adjective-noun phrase. - **Upotrěbljenje / inflection:** Feminine logika; genitive deontičnoj logiky and plural deontične logiky. - **Kirilična forma:** `деонтична логика` - **Argumentacija / rationale:** Deontična logika retains the internationally stable specialist name, while the immediately adjacent obligation definition makes it usable without Greek etymological knowledge. The source's quotation marks are preserved in running prose. - **Uvěrjenost / status:** 0.89 (high); `provisional`; revision `OLISV-T0329-r0001`. - **Slovjanske sravnenja / comparanda:** ru: деонтическая логика; uk: деонтична логіка; pl: logika deontyczna; cs: deontická logika; bcs: deontička logika; деонтичка логика; bg: деонтична логика. - **Dokazy / evidence:** OL-FOL-BEYOND-OTHER-LOGICS (lines 30-32); ISV-DICT-LIVE-20260825 (dictionary_id=8933; lemma=logika; gloss=logic); ISV-DICT-LIVE-20260825 (dictionary_id=95; lemma=obvęzȯk; gloss=duty, obligation); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** logika obvęzkov: The descriptive phrase is readable but too narrow for a field that can also formalize permissions and prohibitions; the source itself names the field deontic. - **Neizvěstnost / uncertainty:** The frozen dictionary does not directly list the deontic adjective; the international form is source-bound and edition-level. ## OLISV-T0308 · logic.diamond-operator - **English lemma / sense:** diamond operator — The modal operator Diamond, written ◇, expressing possibility and defined in the source as not-Box-not. - **Medžuslovjansky:** `operator možlivosti`; lemma `operator možlivosti`; masculine noun phrase. - **Upotrěbljenje / inflection:** Masculine operator; genitive operatora možlivosti. The symbol is written $\Diamond$. - **Kirilična forma:** `оператор можливости` - **Argumentacija / rationale:** Operator možlivosti makes the Diamond symbol's possible reading explicit and retains the exact abbreviation formula. The term is paired with operator neobhodnosti, not treated as an independent translation witness. - **Uvěrjenost / status:** 0.9 (high); `provisional`; revision `OLISV-T0308-r0001`. - **Slovjanske sravnenja / comparanda:** ru: оператор возможности (◇); uk: оператор можливості (◇); pl: operator możliwości (◇); cs: operátor možnosti (◇); bcs: operator mogućnosti (◇); bg: оператор за възможност (◇). - **Dokazy / evidence:** OL-FOL-BEYOND-MODAL-LOGICS (lines 36-38 and 59-64); ISV-DICT-LIVE-20260825 (dictionary_id=2752; lemma=možlivosť; gloss=possibility); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** operator diamanta: A shape-based calque is less informative than the direct possibility function and risks treating the symbol as a geometric object. - **Neizvěstnost / uncertainty:** The source's consistency gloss in provability logic is a pedagogical simplification; this entry names the general modal operator only. ## OLISV-T0010 · logic.discipline - **English lemma / sense:** logic — Logic as the discipline or philosophical notion concerned with valid reasoning, and contextually an individuated formal logical framework. The formal-system sense is recorded more explicitly under T0222. - **Medžuslovjansky:** `logika`; lemma `logika`; feminine noun. - **Upotrěbljenje / inflection:** Feminine noun; genitive singular logiky. Use logika for the discipline and in compounds such as logika prvogo reda. - **Kirilična forma:** `логика` - **Argumentacija / rationale:** The international lemma remains directly listed and fully convergent across the six comparison traditions. OLP-0175 deliberately moves between the discipline or philosophical notion and an individuated formal framework; preserving one lexical head records that controlled polysemy while T0222 carries the explicit logical-system profile. - **Uvěrjenost / status:** 0.98 (high); `provisional`; revision `OLISV-T0010-r0002`. - **Slovjanske sravnenja / comparanda:** ru: логика; uk: логіка; pl: logika; cs: logika; bcs: logika; bg: логика. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[10431]; dictionary_id=8933); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** razumovanje: This denotes reasoning as an activity rather than logic as a formal discipline. - **Neizvěstnost / uncertainty:** The passage presents several philosophical conceptions without selecting one definition of logic.; Use T0222 when the explicit system head or its defeasible component profile is the point. ## OLISV-T0114 · logic.disjunction - **English lemma / sense:** disjunction — The disjunction connective, classically truth-functional and constructively interpreted as a proof of one disjunct together with information identifying it. - **Medžuslovjansky:** `disjunkcija`; lemma `disjunkcija`; feminine noun. - **Upotrěbljenje / inflection:** Genitive disjunkcije; qualify as inclusive if contrast with exclusive disjunction matters. - **Kirilična forma:** `дисјункција` - **Argumentacija / rationale:** International specialist form converges across all comparison languages. The dedicated OLP-0179 unit now broadens the current sense while the earlier revision remains preserved as scope provenance. - **Uvěrjenost / status:** 0.9 (high); `provisional`; revision `OLISV-T0114-r0002`. - **Slovjanske sravnenja / comparanda:** ru: дизъюнкция; uk: диз'юнкція; pl: alternatywa; dysjunkcja; cs: disjunkce; bcs: disjunkcija; дисјункција; bg: дизюнкция. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 97-107 and 216); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** logično ili: The descriptive reading is clear but not a stable terminological head for the connective. - **Neizvěstnost / uncertainty:** No exact frozen dictionary row attests the logic-specific noun.; Earlier narrower sense wording remains preserved in the superseded revision. ## OLISV-T0291 · logic.double-negation-translation - **English lemma / sense:** double-negation translation — The inductively defined map sending classical formulas to intuitionistic formulas by inserting double negations in specified clauses. - **Medžuslovjansky:** `prěvod dvojnoj negacije`; lemma `prěvod dvojnoj negacije`; masculine noun with genitive phrase. - **Upotrěbljenje / inflection:** Masculine prěvod; genitive prěvoda dvojnoj negacije. - **Kirilična forma:** `прєвод двојној негације` - **Argumentacija / rationale:** The target's prěvod dvojnoj negacije directly names the map, while the displayed inductive clauses prevent confusion with merely applying negation twice to one formula. - **Uvěrjenost / status:** 0.94 (high); `provisional`; revision `OLISV-T0291-r0001`. - **Slovjanske sravnenja / comparanda:** ru: перевод двойного отрицания; uk: переклад подвійного заперечення; pl: przekład podwójnej negacji; cs: překlad dvojité negace; bcs: prijevod dvostruke negacije; превод двоструке негације; bg: превод с двойно отрицание. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 135-178); ISV-DICT-LIVE-20260825 (dictionary_id=20073; lemma=prěvod; gloss=translation); ISV-DICT-LIVE-20260825 (dictionary_id=476; lemma=dvojny; gloss=double); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** prěklad dvojnoj negacije: Also means translation, but prěvod is the established edition head for a formal formula transformation. - **Neizvěstnost / uncertainty:** No direct dictionary negation noun is pinned; that component inherits the established T0113 logical terminology. ## OLISV-T0060 · logic.eigenvariable - **English lemma / sense:** eigenvariable — A fresh variable or constant constrained not to occur above the relevant quantifier-rule application. - **Medžuslovjansky:** `eigenprěměnna`; lemma `eigenprěměnna`; noun. - **Upotrěbljenje / inflection:** Feminine compound noun; retain eigen- as the internationally recognizable technical modifier and decline prěměnna regularly. - **Kirilična forma:** `еигенпрємєнна` - **Argumentacija / rationale:** The international eigen- modifier sharply distinguishes this proof-theoretic freshness condition from ordinary variable ownership, while prěměnna remains transparent across the edition; the text always explains the condition on first use. - **Uvěrjenost / status:** 0.55 (medium); `provisional`; revision `OLISV-T0060-r0001`. - **Slovjanske sravnenja / comparanda:** ru: собственная переменная; uk: власна змінна; pl: zmienna własna; cs: vlastní proměnná; bcs: svojstvena varijabla; bg: собствена променлива. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** svoja prěměnna: A literal own-variable compound is more Slavic-looking but can be misread as possession and does not uniquely identify the freshness side condition. - **Neizvěstnost / uncertainty:** No official Interslavic dictionary entry for eigenvariable was found in the pinned evidence, and the national Slavic comparanda do not converge on the retained international modifier. ## OLISV-T0234 · logic.embed - **English lemma / sense:** embed — Faithfully encode a many-sorted logical system inside first-order logic so that its relevant syntactic and semantic structure is preserved. - **Medžuslovjansky:** `vgraditi`; lemma `vgraditi`; transitive perfective verb. - **Upotrěbljenje / inflection:** Perfective vgraditi; use vgraditi mnogosortnu logiku v logiku prvogo reda. The established imperfective family is vgradžati. - **Kirilična forma:** `вградити` - **Argumentacija / rationale:** The exact verb already has two accepted edition precedents and denotes a faithful inclusion more precisely than generic translation. - **Uvěrjenost / status:** 0.72 (medium); `provisional`; revision `OLISV-T0234-r0001`. - **Slovjanske sravnenja / comparanda:** ru: встроить; вложить; uk: вбудувати; вкласти; pl: osadzić; cs: vnořit; bcs: ugraditi; уградити; bg: вгради; вложи. - **Dokazy / evidence:** OL-SET-INFINITE-DEDEKIND-ISV (line 42; accepted target SHA-256 DBDDC781B92AB580F9C6C4142D54C9A155E7F0DF1D2D1D6A3BABCE802DC5B8E3); OL-FOL-THEORIES-EXPRESSING-RELATIONS-ISV (line 39; accepted target SHA-256 5D59221001D51AC7CFD0C338521999AB4CCE0E00A36BE3A755AC22869668AA30); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** interpretovati: Describes semantic interpretation, not necessarily a faithful encoding.; prěvoditi: Generic translation loses the embedding claim. - **Neizvěstnost / uncertainty:** The national full verbs are editorial specialist comparanda; no direct frozen vgraditi lemma is claimed. ## OLISV-T0375 · logic.empty-string - **English lemma / sense:** empty string — The unique length-zero finite string in the free monoid of words over the one-symbol alphabet, used here as the interpretation of zero. - **Medžuslovjansky:** `prazdny niz`; lemma `prazdny niz`; masculine adjective-noun phrase. - **Upotrěbljenje / inflection:** Masculine singular prazdny niz; genitive prazdnogo niza. Reserve prazdno množstvo for the set with no members; here the object is the identity string under concatenation. - **Kirilična forma:** `праздны низ` - **Argumentacija / rationale:** Prazdny niz extends the established technical head niz simbolov (OLISV-T0133) and keeps the object visibly distinct from prazdno množstvo (OLISV-T0190). The direct Ukrainian witness shows that empty word is also conventional; the edition chooses string because this passage explicitly presents finite strings and concatenation, while recording the word convention as an alternative rather than erasing it. The effective source now uses Lambda, matching the same Open Logic revision's explicit empty-string notation. - **Uvěrjenost / status:** 0.82 (medium); `provisional`; revision `OLISV-T0375-r0001`. - **Slovjanske sravnenja / comparanda:** ru: пустая строка; пустое слово; uk: порожнє слово; pl: pusty ciąg; słowo puste; cs: prázdný řetězec; prázdné slovo; bcs: prazan niz; prazna riječ; bg: празен низ; празна дума. - **Dokazy / evidence:** OL-MODEL-ARITHMETIC-INTRODUCTION (lines 24-34); OL-SETS-IMPORTANT-SETS (lines 46-54); ISV-DICT-LIVE-20260825 (wordList[6101]; dictionary_id=16335; lemma=pråzdny; gloss=empty, idle); UK-KNU-LOGIC-FOUNDATIONS-2020 (physical pages 15 and 44 / extracted lines 582 and 1880); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic, standard flavorization) - **Alternativy / alternatives:** prazdno slovo: Directly supported as a Ukrainian formal-language convention and acceptable as an explanatory synonym, but it would switch the passage's stated string ontology to word terminology and weaken continuity with OLISV-T0133.; prazdno množstvo: The source uses the empty-string symbol as an element and concatenation identity; an empty set has no elements and is a different mathematical object already covered by OLISV-T0190. - **Neizvěstnost / uncertainty:** No direct pinned full-phrase national source in this packet uses the selected string noun.; The immutable OLP-0192 source uses the empty-set glyph, but the hash-bound effective source corrects it to Lambda using the project's own explicit same-revision notation; both states remain auditable. ## OLISV-T0312 · logic.epistemic - **English lemma / sense:** epistemic logic — A modal application in which Box A can express an agent's knowledge or belief about A. - **Medžuslovjansky:** `epistemična logika`; lemma `epistemična logika`; feminine adjective-noun phrase. - **Upotrěbljenje / inflection:** Feminine logika; genitive epistemičnoj logiky. - **Kirilična forma:** `епистемична логика` - **Argumentacija / rationale:** Epistemična logika follows the international epistemic label and preserves the source's paired knowledge/belief examples. The wording does not pretend that knowledge and belief are formally identical. - **Uvěrjenost / status:** 0.85 (high); `provisional`; revision `OLISV-T0312-r0001`. - **Slovjanske sravnenja / comparanda:** ru: эпистемическая логика; uk: епістемічна логіка; pl: logika epistemiczna; cs: epistemická logika; bcs: epistemička logika; bg: епистемична логика. - **Dokazy / evidence:** OL-FOL-BEYOND-MODAL-LOGICS (lines 61-62); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** logika znanja: A native paraphrase is readable but too narrow for the source, which explicitly includes belief and the broader epistemic application. - **Neizvěstnost / uncertainty:** The source places knowledge and belief together; the canon records that pedagogical conflation instead of silently choosing a doxastic subtheory. ## OLISV-T0264 · logic.equation - **English lemma / sense:** equation — A displayed equality governing the terms introduced by the higher-order term constructors. - **Medžuslovjansky:** `ravnost`; lemma `ravnost`; feminine noun. - **Upotrěbljenje / inflection:** Feminine ravnost; plural ravnosti, genitive ravnosti. The dictionary lemma is råvnosť (with U+00E5 å); the edition uses the normalized ravnost surface. - **Kirilična forma:** `равност` - **Argumentacija / rationale:** The source calls the displayed recursive identities equations, while the pinned dictionary directly supplies the equality family. Ravnost is therefore recorded as the edition's normalized equality/equation head, with the source locator preserving the distinction between an equation as a display and identity as a logical relation. - **Uvěrjenost / status:** 0.85 (high); `provisional`; revision `OLISV-T0264-r0002`. - **Slovjanske sravnenja / comparanda:** ru: уравнение; uk: рівність; pl: równanie; cs: rovnice; bcs: jednačina; једначина; bg: уравнение. - **Dokazy / evidence:** OL-FOL-BEYOND-HIGHER-ORDER-LOGIC (lines 75-93); ISV-DICT-LIVE-20260825 (dictionary_id=30091; lemma=råvnosť; gloss=equality, evenness, parity); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** identičnost: Already reserved for the logical identity relation and would collapse equation syntax with identity semantics.; råvnosť: The literal dictionary spelling is preserved in evidence, but the current standard-Latin surface normalizes å to a for this edition. - **Neizvěstnost / uncertainty:** The English word equation is often lexicalized as a separate root from equality; the selected head is an editorial bridge and not a claim of one-to-one national equivalence.; The r0001 record is preserved as adverse provenance for the evidence correction. ## OLISV-T0288 · logic.excluded-middle - **English lemma / sense:** law of excluded middle — The classical principle asserting A or not-A for every formula A. - **Medžuslovjansky:** `zakon izključenogo tretjego`; lemma `zakon izključenogo tretjego`; masculine noun with genitive adjective-number phrase. - **Upotrěbljenje / inflection:** Masculine zakon; genitive zakona izključenogo tretjego. - **Kirilična forma:** `закон изкљученого третјего` - **Argumentacija / rationale:** The transparent Slavic calque mirrors the source's displayed A-or-not-A principle and uses three direct lexical components. - **Uvěrjenost / status:** 0.98 (high); `provisional`; revision `OLISV-T0288-r0001`. - **Slovjanske sravnenja / comparanda:** ru: закон исключённого третьего; uk: закон виключеного третього; pl: prawo wyłączonego środka; cs: zákon vyloučeného třetího; bcs: zakon isključenja trećeg; закон искључења трећег; bg: закон за изключеното трето. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 114-126); ISV-DICT-LIVE-20260825 (dictionary_id=1901; lemma=zakon; gloss=law, act (law), lex); ISV-DICT-LIVE-20260825 (dictionary_id=482; lemma=izključiti; gloss=exclude, except); ISV-DICT-LIVE-20260825 (dictionary_id=439; lemma=treťji; gloss=third); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** princip A ili ne-A: A notation-based paraphrase is useful pedagogically but is not the conventional canonical name. - **Neizvěstnost / uncertainty:** West Slavic traditions sometimes lexicalize the middle rather than the third; the edition follows the broader East/South third pattern. ## OLISV-T0162 · logic.existential-generalization - **English lemma / sense:** existential generalization — The inference from A(a) to there exists x A(x), sound under the stated nonempty-domain and referring-name assumptions. - **Medžuslovjansky:** `eksistencialna generalizacija`; lemma `eksistencialna generalizacija`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive singular eksistencialnoj generalizacije. Use the term only for the inference pattern, not for existential quantification generally. - **Kirilična forma:** `ексистенциална генерализација` - **Argumentacija / rationale:** The international compound is nearly pan-Slavic and pairs a normalized standard-Latin existential adjective with the directly registered generalizacija head. The source supplies the exact inference and its semantic preconditions. - **Uvěrjenost / status:** 0.88 (high); `provisional`; revision `OLISV-T0162-r0001`. - **Slovjanske sravnenja / comparanda:** ru: экзистенциальное обобщение; uk: екзистенційне узагальнення; pl: generalizacja egzystencjalna; cs: existenční generalizace; bcs: egzistencijalna generalizacija; егзистенцијална генерализација; bg: екзистенциално обобщение. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-DICT-LIVE-20260825 (wordList[6493]; dictionary_id=37680); ISV-DICT-LIVE-20260825 (wordList[7564]; dictionary_id=35427); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** eksistencialno obobćenje: The native generalization head is possible but less uniformly recognizable across the six specialist traditions than the international noun.; egzistencijaľna generalizacija: This follows the raw frozen adjective row but retains etymological soft-sign spelling and a less broadly normalized initial cluster for the public basic-Latin reader. - **Neizvěstnost / uncertainty:** The frozen adjective is recorded as egzistencijaľny; the preferred surface is a standard-Latin specialist normalization supported by comparison forms, not a direct dictionary spelling.; The inference is sound only under the semantic assumptions recorded by the source and entry sense. ## OLISV-T0118 · logic.existential-quantifier - **English lemma / sense:** existential quantifier — A quantifier asserting that its scope holds for at least one domain object. - **Medžuslovjansky:** `eksistencialny kvantifikator`; lemma `eksistencialny kvantifikator`; masculine noun phrase. - **Upotrěbljenje / inflection:** Genitive eksistencialnogo kvantifikatora; associated with the exists symbol. - **Kirilična forma:** `ексистенциалны квантификатор` - **Argumentacija / rationale:** International modifier plus canonical quantifier is broadly recognizable and semantically precise. - **Uvěrjenost / status:** 0.89 (high); `provisional`; revision `OLISV-T0118-r0001`. - **Slovjanske sravnenja / comparanda:** ru: квантор существования; uk: квантор існування; pl: kwantyfikator egzystencjalny; cs: existenční kvantifikátor; bcs: egzistencijalni kvantifikator; егзистенцијални квантификатор; bg: квантор за съществуване. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** bytnostny kvantifikator: A native calque is not established and risks metaphysical rather than binding semantics. - **Neizvěstnost / uncertainty:** The complete compound is not a direct frozen dictionary headword. ## OLISV-T0189 · logic.explicit-definition - **English lemma / sense:** explicit definition — An axiom that introduces a symbol by stating an equivalent condition formulated with previously available vocabulary. - **Medžuslovjansky:** `eksplicitna definicija`; lemma `eksplicitna definicija`; feminine noun phrase. - **Upotrěbljenje / inflection:** The adjective agrees with definicija: genitive eksplicitnoj definicije; plural eksplicitne definicije. - **Kirilična forma:** `експлицитна дефиниција` - **Argumentacija / rationale:** Eksplicitna definicija is internationally recognizable and avoids making the formal notion depend on javny, whose frozen primary sense is public. The source supplies the exact definitional role of the last Peano axiom. - **Uvěrjenost / status:** 0.82 (high); `provisional`; revision `OLISV-T0189-r0001`. - **Slovjanske sravnenja / comparanda:** ru: явное определение; uk: явне визначення; pl: definicja jawna; cs: explicitní definice; bcs: eksplicitna definicija; експлицитна дефиниција; bg: явна дефиниция. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[4862]; dictionary_id=2624; lemma=definicija; gloss=definition); ISV-DICT-LIVE-20260825 (wordList[6530]; dictionary_id=17625; lemma=jednoznačny; gloss includes explicit); ISV-DICT-LIVE-20260825 (wordList[13639]; dictionary_id=8241; lemma=javny; gloss=public); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** javno opreděljenje: This calque is transparent to East Slavic readers, but javny is primarily public in the frozen Interslavic row and opreděljenje is not the accepted dictionary head for definition. - **Neizvěstnost / uncertainty:** The selected adjective is an editorial internationalism; the frozen dictionary supplies only adjacent explicit/unambiguous and national comparison evidence. ## OLISV-T0085 · logic.expressibility - **English lemma / sense:** expressibility; expressible — The capacity of a formal language or theory to state a property by a sentence or set of sentences. - **Medžuslovjansky:** `izrazimost`; lemma `izrazimost`; feminine abstract noun. - **Upotrěbljenje / inflection:** Use izrazimy for the adjective and izraziti for the perfective verb in formal-language contexts. - **Kirilična forma:** `изразимост` - **Argumentacija / rationale:** A regular abstraction from the direct express aspect pair maps transparently onto the language–property relation and avoids stylistic expressiveness. - **Uvěrjenost / status:** 0.69 (medium); `provisional`; revision `OLISV-T0085-r0001`. - **Slovjanske sravnenja / comparanda:** ru: выразимость; uk: виражуваність; виразність; pl: wyrażalność; cs: vyjádřitelnost; bcs: izrazivost; bg: изразимост. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[6564-6565]; dictionary_id=682,2609); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** izraznost: The direct noun means emphasis or stylistic expressiveness, not logical expressibility.; opreděljivost: Definability is related but stricter and needs its own sense entry. - **Neizvěstnost / uncertainty:** The source informally groups one-sentence expressibility and axiomatizability by a theory. ## OLISV-T0093 · logic.expression - **English lemma / sense:** expression — Any syntactic object of the formal language, including terms and formulas. - **Medžuslovjansky:** `izraz`; lemma `izraz`; masculine noun. - **Upotrěbljenje / inflection:** Genitive singular izraza; use as the superordinate syntactic category, not merely an utterance. - **Kirilična forma:** `израз` - **Argumentacija / rationale:** Izraz is directly attested as term, phrase, and expression and is maximally recognizable. - **Uvěrjenost / status:** 0.88 (high); `provisional`; revision `OLISV-T0093-r0001`. - **Slovjanske sravnenja / comparanda:** ru: выражение, фраза, термин; uk: вираз, термін; pl: wyrażenie, wyraz, zwrot, fraza, ekspresja; cs: výraz, termín, fráze; bcs: izraz, izreka, fraza; израз, фраза; bg: израз. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[17058]; dictionary_id=8115); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** izraženje: The verbal noun more readily denotes the act or result of expressing than a formal syntactic object. - **Neizvěstnost / uncertainty:** The dictionary lemma is broader than the formal category. ## OLISV-T0169 · logic.expression-complexity - **English lemma / sense:** complexity of an expression — The recursively determined structural complexity of a term or formula, used as the induction measure in proofs by construction. - **Medžuslovjansky:** `složenost izraza`; lemma `složenost izraza`; feminine noun phrase. - **Upotrěbljenje / inflection:** Use po složenosti terma and po složenosti formuly when the expression kind is explicit; složenost is the project running-text normalization of dictionary složenosť. - **Kirilična forma:** `сложеност израза` - **Argumentacija / rationale:** Složenost is directly attested and broadly transparent across East, West, and South Slavic traditions; the genitive izraza makes the recursive syntactic sense explicit while allowing contextual terma and formuly in prose. - **Uvěrjenost / status:** 0.91 (high); `provisional`; revision `OLISV-T0169-r0001`. - **Slovjanske sravnenja / comparanda:** ru: сложность выражения; uk: складність виразу; pl: złożoność wyrażenia; cs: složitost výrazu; bcs: složenost izraza; сложеност израза; bg: сложност на израза. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[3828]; dictionary_id=12336; lemma=složenosť; gloss=complexity, complication, difficulty); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** kompleksnost izraza: The international stem is recognizable but less uniformly supported by the frozen dictionary row and can suggest a broader systems notion rather than the recursive construction measure. - **Neizvěstnost / uncertainty:** The dictionary head has broad ordinary senses in addition to the precise recursive logic sense.; The running edition suppresses the optional final soft marker found in the frozen dictionary surface složenosť. ## OLISV-T0173 · logic.extensionality - **English lemma / sense:** extensionality — The semantic invariance principle that the satisfaction of a formula depends only on the common domain and on the interpretations and variable assignments for symbols and variables actually occurring in that formula. - **Medžuslovjansky:** `ekstensionalnost`; lemma `ekstensionalnost`; feminine abstract noun. - **Upotrěbljenje / inflection:** Decline as a feminine consonant noun: genitive ekstensionalnosti; use ekstensionalny for the adjective. Relevantnost may explain the source synonym but is not the preferred technical head. - **Kirilična forma:** `екстенсионалност` - **Argumentacija / rationale:** Ekstensionalnost retains the internationally recognizable extens- technical family and follows the frozen Interslavic dictionary's s-normalization, reinforced by Russian, Ukrainian, and Polish specialist comparanda. Czech, BCS, and Bulgarian z-forms remain explicit adverse evidence. Open Logic supplies the exact semantic-invariance definition, preventing the internationalism from floating as an unexplained label. - **Uvěrjenost / status:** 0.78 (medium); `provisional`; revision `OLISV-T0173-r0001`. - **Slovjanske sravnenja / comparanda:** ru: экстенсиональность; uk: екстенсіональність; pl: ekstensjonalność; cs: extenzionalita; bcs: ekstenzionalnost; екстензионалност; bg: екстензионалност. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[6583]; dictionary_id=37683; lemma=ekstensivny; gloss=extensive); ISV-DICT-LIVE-20260825 (wordList[9397]; dictionary_id=36332; lemma=intensivnosť; gloss=intensity); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** ekstenzionalnost: The z-form is strong in Czech, BCS, and Bulgarian and remains fully intelligible, but the pinned Interslavic dictionary normalizes the parallel extens- and intens- international roots with s, matching Russian, Ukrainian, and Polish specialist practice.; relevantnost: The source gives relevance as a secondary name, but outside this proposition it has broader pragmatic and proof-theoretic senses and therefore does not uniquely identify semantic extensionality.; razširjenost: A native extension-family calque suggests spatial widening or dissemination and does not transparently identify the model-theoretic invariance principle. - **Neizvěstnost / uncertainty:** No direct Interslavic dictionary lemma for logical extensionality was found in the pinned response.; Russian, Ukrainian, and Polish favor s, whereas Czech, BCS, and Bulgarian favor z; the selected s is an editorial project normalization, not a claim that the alternatives are wrong.; The source's informal phrase size of the domain conflicts with the formal same-domain premise and is translated as the domain itself; the unmodified source wording remains preserved as adverse evidence. ## OLISV-T0110 · logic.falsity - **English lemma / sense:** falsity — The false truth value or propositional constant denoting it. - **Medžuslovjansky:** `ložnost`; lemma `ložnost`; feminine noun. - **Upotrěbljenje / inflection:** Genitive ložnosti; standard-Latin normalization of dictionary lȯžnosť. - **Kirilična forma:** `ложност` - **Argumentacija / rationale:** Direct falsity lemma and strong East/South cognacy; the source fixes the logical truth-value sense. - **Uvěrjenost / status:** 0.78 (medium); `provisional`; revision `OLISV-T0110-r0001`. - **Slovjanske sravnenja / comparanda:** ru: ложность, фальшивость, ошибочность; uk: помилковість, фальшивість; pl: fałszywość; cs: lživost, falešnost; bcs: lažnost; лажност; bg: лъжливост, фалшивост. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[6703]; dictionary_id=32196); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** neistina: The transparent antonym is retained as a reader-facing synonym but does not distinguish falsehood from the technical truth value as sharply. - **Neizvěstnost / uncertainty:** Polish and Czech commonly prefer fałszywość/falešnost rather than the lož- family. ## OLISV-T0257 · logic.finite-type - **English lemma / sense:** finite type — A type generated from the base natural-number type by the finite type-construction clauses. - **Medžuslovjansky:** `konečny tip`; lemma `konečny tip`; masculine adjective-noun phrase. - **Upotrěbljenje / inflection:** Plural konečne tipy; genitive konečnogo tipa. Use the normalized konečny spelling in the edition, although the dictionary row is konėčny. - **Kirilična forma:** `конечны тип` - **Argumentacija / rationale:** The source defines a closed class of finite types. The dictionary supplies the type head, a finiteness noun, and an adjective family; the specialist finite sense is fixed by the Open Logic induction clauses rather than by the general gloss final/end alone. - **Uvěrjenost / status:** 0.9 (high); `provisional`; revision `OLISV-T0257-r0002`. - **Slovjanske sravnenja / comparanda:** ru: конечный тип; uk: скінченний тип; pl: typ skończony; cs: konečný typ; bcs: konačan tip; коначан тип; bg: краен тип. - **Dokazy / evidence:** OL-FOL-BEYOND-HIGHER-ORDER-LOGIC (lines 23-28 and 44-55); ISV-DICT-LIVE-20260825 (dictionary_id=8557; lemma=konėčny; gloss=final, end, ultimate); ISV-DICT-LIVE-20260825 (dictionary_id=3224; lemma=tip; gloss=type, kind); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3); ISV-DICT-LIVE-20260825 (dictionary_id=17676; lemma=konėčnosť; gloss=finiteness, finality) - **Alternativy / alternatives:** konėčnosť tip: An abstract finiteness noun cannot serve as the attributive adjective required by the source's formation rule.; ograničeny tip: Would suggest a bounded cardinality rather than the inductively generated type class. - **Neizvěstnost / uncertainty:** The dictionary's lemma is konėčny while the edition normalizes the surface to konečny; this orthographic normalization is not a claim about national spelling.; The adjective row konėčny is polysemous; konėčnosť supplies the explicit finiteness component.; The r0001 record is preserved as adverse provenance for the evidence correction. ## OLISV-T0090 · logic.first-order - **English lemma / sense:** first-order logic — The formal framework in which quantifiers range over individual objects rather than predicates or sets. - **Medžuslovjansky:** `logika prvogo reda`; lemma `logika prvogo reda`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive singular logiky prvogo reda; use jezyk logiky prvogo reda for a corresponding language. - **Kirilična forma:** `логика првого реда` - **Argumentacija / rationale:** The established edition form follows the dominant Slavic genitive construction, while a dedicated ID separates it from logic as a general discipline. - **Uvěrjenost / status:** 0.94 (high); `provisional`; revision `OLISV-T0090-r0001`. - **Slovjanske sravnenja / comparanda:** ru: логика первого порядка; uk: логіка першого порядку; pl: logika pierwszego rzędu; cs: logika prvního řádu; bcs: logika prvog reda; bg: логика от първи ред. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[10431]; dictionary_id=8933); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** prvoredna logika: The compact calque may read as first-rate logic rather than quantifier order. - **Neizvěstnost / uncertainty:** The complete compound is compositionally established rather than directly listed. ## OLISV-T0096 · logic.first-order-language - **English lemma / sense:** first-order language — A formal language whose variables range over individual objects and whose nonlogical vocabulary has fixed finite arities. - **Medžuslovjansky:** `jezyk logiky prvogo reda`; lemma `jezyk logiky prvogo reda`; masculine noun phrase. - **Upotrěbljenje / inflection:** Genitive jezyka logiky prvogo reda; the longer form keeps the logical restriction explicit. - **Kirilična forma:** `језык логикы првого реда` - **Argumentacija / rationale:** Transparent composition reuses the canonical first-order-logic term and the direct language lemma. - **Uvěrjenost / status:** 0.84 (medium); `provisional`; revision `OLISV-T0096-r0001`. - **Slovjanske sravnenja / comparanda:** ru: язык логики первого порядка; uk: мова логіки першого порядку; pl: język logiki pierwszego rzędu; cs: jazyk logiky prvního řádu; bcs: jezik logike prvog reda; језик логике првог реда; bg: език на логиката от първи ред. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[9987]; dictionary_id=541); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** prvoredny jezyk: The compact adjective is less immediately interpretable and is not established by the frozen evidence. - **Neizvěstnost / uncertainty:** The complete compound is editorial rather than a direct dictionary headword. ## OLISV-T0298 · logic.forcing-relation - **English lemma / sense:** forcing relation — The inductively defined relation stating that a formula is true at a world of a Kripke structure. - **Medžuslovjansky:** `odnošenje forsiranja`; lemma `odnošenje forsiranja`; neuter noun with genitive verbal noun. - **Upotrěbljenje / inflection:** Neuter odnošenje; genitive odnošenja forsiranja. - **Kirilična forma:** `одношење форсирања` - **Argumentacija / rationale:** Odnošenje forsiranja preserves the source's named technical relation and direct relation head. The ordinary force row is adverse evidence only: the inductive Kripke clauses, not coercion, define the specialist sense. - **Uvěrjenost / status:** 0.74 (medium); `provisional`; revision `OLISV-T0298-r0001`. - **Slovjanske sravnenja / comparanda:** ru: отношение вынуждения; uk: відношення форсування; pl: relacja wymuszania; cs: relace vynucování; bcs: relacija forsiranja; релација форсирања; bg: отношение на форсиране. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 207-218); ISV-DICT-LIVE-20260825 (dictionary_id=1992; lemma=odnošeńje; gloss=relation, relationship, attitude, ratio, proportion); ISV-DICT-LIVE-20260825 (dictionary_id=2136; lemma=prinuditi; gloss=force); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** odnošenje zadovoljenja: Would conflate world-indexed forcing with the already established model satisfaction relation and hide the source's terminology. - **Neizvěstnost / uncertainty:** Forsiranje is an editorial international derivative with uneven national uptake; the canon definition and notation must accompany it. ## OLISV-T0317 · logic.formal - **English lemma / sense:** formal logic — A logic presented through an explicit formal syntax, deductive apparatus, and semantics rather than only ordinary-language argument. - **Medžuslovjansky:** `formalna logika`; lemma `formalna logika`; feminine adjective-noun phrase. - **Upotrěbljenje / inflection:** Feminine logika; genitive formalnoj logiky and plural formalne logiky. - **Kirilična forma:** `формална логика` - **Argumentacija / rationale:** Formalna logika uses the universally transparent formal/logika pair and the edition's regular adjective agreement. The source supplies the field sense; the normalized l spelling avoids presenting the dictionary's soft-l notation as mandatory in running text. - **Uvěrjenost / status:** 0.96 (high); `provisional`; revision `OLISV-T0317-r0001`. - **Slovjanske sravnenja / comparanda:** ru: формальная логика; uk: формальна логіка; pl: logika formalna; cs: formální logika; bcs: formalna logika; формална логика; bg: формална логика. - **Dokazy / evidence:** OL-FOL-BEYOND-OTHER-LOGICS (line 22); ISV-DICT-LIVE-20260825 (dictionary_id=20376; lemma=formaľny; gloss=formal); ISV-DICT-LIVE-20260825 (dictionary_id=8933; lemma=logika; gloss=logic); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** formaľna logika: This mirrors the frozen dictionary's marked soft-l surface, but the running edition normalizes the international adjective to formalna for consistency and accessibility. - **Neizvěstnost / uncertainty:** The orthographic normalization from formaľny to formalny is an edition choice and is not a claim that the frozen lemma is erroneous. ## OLISV-T0102 · logic.formation-rule - **English lemma / sense:** formation rule — A recursive clause specifying how well-formed expressions may be constructed. - **Medžuslovjansky:** `pravilo tvorjenja`; lemma `pravilo tvorjenja`; neuter noun phrase. - **Upotrěbljenje / inflection:** Genitive pravila tvorjenja; use collectively for the inductive grammar clauses. - **Kirilična forma:** `правило творјења` - **Argumentacija / rationale:** The native compound is compositionally transparent across all three Slavic zones. - **Uvěrjenost / status:** 0.74 (medium); `provisional`; revision `OLISV-T0102-r0001`. - **Slovjanske sravnenja / comparanda:** ru: правило образования; uk: правило побудови; pl: reguła tworzenia; cs: pravidlo tvorby; bcs: pravilo tvorbe; правило творбе; bg: правило за образуване. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** formacijsko pravilo: The international adjective is shorter but less immediately transparent to a broad receptive audience. - **Neizvěstnost / uncertainty:** The complete phrase is not directly attested in the frozen dictionary. ## OLISV-T0150 · logic.formation-sequence - **English lemma / sense:** formation sequence — A finite ordered sequence of language strings ending in a target term or formula, with each member primitive or obtained from earlier members by an applicable formation clause. - **Medžuslovjansky:** `poslědovnost formovanja`; lemma `poslědovnost formovanja`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive poslědovnosti formovanja; typed use forms are termova poslědovnost formovanja and formulova poslědovnost formovanja. - **Kirilična forma:** `послєдовност формовања` - **Argumentacija / rationale:** Poslědovnost formovanja preserves the established wording of the accepted propositional-logic unit and transparently distinguishes an ordered derivational history from the canon's niz simbolov, which names a string rather than a sequence of construction stages. Formovanje is directly dictionary-backed and broadly recognizable across the comparison traditions. - **Uvěrjenost / status:** 0.86 (high); `provisional`; revision `OLISV-T0150-r0001`. - **Slovjanske sravnenja / comparanda:** ru: последовательность образования; uk: послідовність побудови; pl: ciąg tworzenia; cs: posloupnost tvorby; bcs: niz tvorbe; низ творбе; bg: последователност на образуване. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-DICT-LIVE-20260825 (wordList[7252]; dictionary_id=25511); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** niz tvorjenja: This compact alternative reuses two canonical components, but niz already names a symbol string in this edition and the alternative would silently rename a concept already used throughout the accepted propositional-logic formation-sequence unit.; sekvencija formovanja: The international head is recognizable, but it needlessly splits the established edition vocabulary and is less transparent than the accepted poslědovnost surface for many Slavic readers. - **Neizvěstnost / uncertainty:** The complete specialist compound is an edition-level selection rather than a direct dictionary headword.; National traditions divide between sequence/poslědovnost, ciąg/niz, and formation/construction/tvorba heads; the formal definition fixes the sense.; No official or native certification is claimed for the complete specialist compound. ## OLISV-T0011 · logic.formula - **English lemma / sense:** formula — A well-formed expression of a formal language built according to its formation rules. - **Medžuslovjansky:** `formula`; lemma `formula`; feminine noun. - **Upotrěbljenje / inflection:** Feminine noun; genitive singular formuly, nominative plural formuly. Modifiers agree, as in atomna formula. - **Kirilična forma:** `формула` - **Argumentacija / rationale:** Formula is directly dictionary-backed, uniform across the comparison languages, and already stable in the inherited mathematical register. - **Uvěrjenost / status:** 0.99 (high); `seed_preferred`; revision `OLISV-T0011-r0001`. - **Slovjanske sravnenja / comparanda:** ru: формула; uk: формула; pl: formuła; cs: formule; bcs: formula; bg: формула. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[7255]; dictionary_id=5181); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** izraz: Izraz is the broader term ‘expression’ and would erase Open Logic’s distinction between formulas and other formal expressions. - **Neizvěstnost / uncertainty:** No specific uncertainty beyond the provisional edition boundary. ## OLISV-T0286 · logic.formulas-as-types - **English lemma / sense:** formulas-as-types paradigm — The computational paradigm that reads formulas as data types and proofs as objects of those types. - **Medžuslovjansky:** `paradigm formuly kako tipy`; lemma `paradigm formuly kako tipy`; masculine noun with nominative explanatory phrase. - **Upotrěbljenje / inflection:** Masculine paradigm; genitive paradigma. Keep the quoted formuly and tipy in nominative plural. - **Kirilična forma:** `парадигм формулы како типы` - **Argumentacija / rationale:** The canon keeps the direct masculine paradigm head from the pinned dictionary and quotes the source's compositional formulas-as-types label, rather than changing the head's gender to match particular national forms. - **Uvěrjenost / status:** 0.93 (high); `provisional`; revision `OLISV-T0286-r0001`. - **Slovjanske sravnenja / comparanda:** ru: парадигма «формулы как типы»; uk: парадигма «формули як типи»; pl: paradygmat «formuły jako typy»; cs: paradigma «formule jako typy»; bcs: paradigma «formule kao tipovi»; парадигма „формуле као типови“; bg: парадигма „формули като типове“. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 108-112); ISV-DICT-LIVE-20260825 (dictionary_id=16999; lemma=paradigm; gloss=paradigm); ISV-DICT-LIVE-20260825 (dictionary_id=5181; lemma=formula; gloss=formula); ISV-DICT-LIVE-20260825 (dictionary_id=3224; lemma=tip; gloss=type, kind); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** paradigma formul i tipov: The feminine head contradicts the pinned Interslavic lemma, while and does not express the source's as relation. - **Neizvěstnost / uncertainty:** National languages usually use a feminine paradigm form; the canon deliberately follows the pinned Interslavic masculine lemma. ## OLISV-T0156 · logic.free-for-substitution - **English lemma / sense:** free for substitution — A term t is admissible for substitution for x in A exactly when no free occurrence of x in A lies in the scope of a quantifier binding a variable that occurs in t. - **Medžuslovjansky:** `možno podstaviti vměsto`; lemma `možno podstaviti vměsto`; invariable modal-infinitive predicate. - **Upotrěbljenje / inflection:** The canonical token omits a copula: use Term t možno podstaviti vměsto x v A. In an existing copular frame, t jest možno podstaviti vměsto x is also permitted. The predicate remains invariant with masculine term and feminine prěměnna. - **Kirilična forma:** `можно подставити вмєсто` - **Argumentacija / rationale:** The modal-infinitive predicate states admissibility without gender agreement and continues the accepted edition wording možno podstaviti ... vměsto. It avoids conflation with free-variable occurrence while preserving the exact capture-avoidance condition. - **Uvěrjenost / status:** 0.76 (medium); `provisional`; revision `OLISV-T0156-r0001`. - **Slovjanske sravnenja / comparanda:** ru: можно подставить вместо; uk: можна підставити замість; pl: można podstawić za; cs: lze dosadit za; bcs: može se uvrstiti umjesto; може се уврстити уместо; bg: може да се подстави вместо. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-DICT-LIVE-20260825 (wordList[13208]; dictionary_id=926); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** svobodny za: A literal calque is gendered and can be misread as the already canonical free-occurrence relation rather than substitution admissibility.; dopustimy za podstanovku: Semantically precise but gendered; it would require agreement changes across term and prěměnna contexts.; podstavlivy: A compact coinage with no attestation in the frozen dictionary or accepted edition. - **Neizvěstnost / uncertainty:** The frozen dictionary does not attest podstaviti or the complete predicate.; The full specialist expression is an edition-level selection, not native or official certification. ## OLISV-T0163 · logic.free-logic - **English lemma / sense:** free logic — A logical system in which singular terms need not denote an object in the quantifier domain and existential generalization therefore requires an existence premise. - **Medžuslovjansky:** `svobodna logika`; lemma `svobodna logika`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive singular svobodnoj logiky. Keep the source's technical non-denoting-term sense distinct from informal freedom or permissiveness. - **Kirilična forma:** `свободна логика` - **Argumentacija / rationale:** Svobodny is directly registered with complete six-language coverage, and the feminine agreement yields the conventional international specialist compound used throughout East and South Slavic traditions and transparently related to West-Slavic equivalents. - **Uvěrjenost / status:** 0.84 (medium); `provisional`; revision `OLISV-T0163-r0001`. - **Slovjanske sravnenja / comparanda:** ru: свободная логика; uk: вільна логіка; pl: logika wolna; cs: volná logika; bcs: slobodna logika; слободна логика; bg: свободна логика. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-DICT-LIVE-20260825 (wordList[7316]; dictionary_id=1977); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** voljna logika: Voljny is possible in ordinary free or voluntary senses but is less continuous with the dominant specialist term and can suggest volition. - **Neizvěstnost / uncertainty:** The complete specialist compound is compositionally rather than directly attested in the frozen dictionary. ## OLISV-T0153 · logic.free-variable-occurrence - **English lemma / sense:** free occurrence of a variable — An occurrence of a variable in a formula that is not bound there by a quantifier occurrence; the status is relative to the containing formula. - **Medžuslovjansky:** `svobodno pojavjenje prěměnnoj`; lemma `svobodno pojavjenje prěměnnoj`; neuter noun phrase. - **Upotrěbljenje / inflection:** Genitive svobodnogo pojavjenja prěměnnoj. Svobodna prěměnna is permitted only as contextual shorthand; the formal property belongs to an occurrence relative to a containing formula. - **Kirilična forma:** `свободно појавјење прємєнној` - **Argumentacija / rationale:** The occurrence-level head states the source's formal object exactly and composes three already established edition components. Svobodno continues the accepted OLP-0144 wording and is directly recognizable across East, West, and South Slavic comparison traditions. - **Uvěrjenost / status:** 0.88 (high); `provisional`; revision `OLISV-T0153-r0001`. - **Slovjanske sravnenja / comparanda:** ru: свободное вхождение переменной; uk: вільне входження змінної; pl: wolne wystąpienie zmiennej; cs: volný výskyt proměnné; bcs: slobodna pojava varijable; слободна појава променљиве; bg: свободно срещане на променлива. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-DICT-LIVE-20260825 (wordList[7316]; dictionary_id=1977); ISV-DICT-LIVE-20260825 (wordList[965]; dictionary_id=10818); ISV-DICT-LIVE-20260825 (wordList[18234]; dictionary_id=35526); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** voljno pojavjenje prěměnnoj: Voljno is broadly recognizable but more polysemous with voluntary, optional, or loose; it would also break the accepted svobodno wording without a semantic gain. - **Neizvěstnost / uncertainty:** National traditions differ in the adjective used for free, but the formal occurrence-relative definition removes ambiguity.; No native or official certification is claimed for the complete specialist compound. ## OLISV-T0267 · logic.full-higher-type-semantics - **English lemma / sense:** full higher-type semantics — The semantics in which a function type ranges over all functions between the corresponding lower-type domains. - **Medžuslovjansky:** `polna semantika vyšših tipov`; lemma `polna semantika vyšših tipov`; feminine noun phrase. - **Upotrěbljenje / inflection:** Feminine semantika; genitive polnoj semantiky vyšših tipov. The adjective polna agrees with semantika. - **Kirilična forma:** `полна семантика вышших типов` - **Argumentacija / rationale:** Polna directly names the source's full/all-functions branch and is the natural qualifier of the higher-type semantics umbrella. The pȯlny dictionary row is normalized to the edition's polny family, while the source's universal all-functions condition remains explicit. - **Uvěrjenost / status:** 0.9 (high); `provisional`; revision `OLISV-T0267-r0002`. - **Slovjanske sravnenja / comparanda:** ru: полная семантика высших типов; uk: повна семантика типів вищого порядку; pl: pełna semantyka wyższych typów; cs: úplná sémantika vyšších typů; bcs: puna semantika viših tipova; пуна семантика виших типова; bg: пълна семантика на висши типове. - **Dokazy / evidence:** OL-FOL-BEYOND-HIGHER-ORDER-LOGIC (lines 102-107); ISV-DICT-LIVE-20260825 (dictionary_id=3141; lemma=pȯlny; gloss=full); ISV-DICT-LIVE-20260825 (dictionary_id=20302; lemma=vysši; gloss=higher); ISV-DICT-LIVE-20260825 (dictionary_id=3224; lemma=tip; gloss=type, kind); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3); ISV-DICT-LIVE-20260825 (dictionary_id=35935; lemma=semantika; gloss=semantics) - **Alternativy / alternatives:** vseobća semantika: Suggests generality rather than the precise quantification over every function between domains.; celosna interpretacija: Changes semantics into interpretation and hides the type-indexed domain structure. - **Neizvěstnost / uncertainty:** The dictionary lemma pȯlny contains a historical vowel mark; the normalized polna surface is an edition convention.; The r0001 record is preserved as adverse provenance for the evidence correction. ## OLISV-T0241 · logic.full-second-order-semantics - **English lemma / sense:** full second-order semantics — Second-order semantics in which, for every arity, the second-order part contains all relations on the first-order domain. - **Medžuslovjansky:** `polna semantika drugogo reda`; lemma `polna semantika drugogo reda`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive polnoj semantiky drugogo reda; use polna semantika when the order is already fixed. - **Kirilična forma:** `полна семантика другого реда` - **Argumentacija / rationale:** The phrase composes two direct dictionary heads and exactly mirrors the source's all-relations condition. The explicit order modifier prevents confusion with first-order semantics or full comprehension alone. - **Uvěrjenost / status:** 0.91 (high); `provisional`; revision `OLISV-T0241-r0002`. - **Slovjanske sravnenja / comparanda:** ru: полная семантика второго порядка; uk: повна семантика другого порядку; pl: semantyka pełnego drugiego rzędu; cs: úplná sémantika druhého řádu; bcs: puna semantika drugog reda; пуна семантика другог реда; bg: пълна семантика от втори ред. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (dictionary_id=3141; lemma=pȯlny; gloss=full); ISV-DICT-LIVE-20260825 (dictionary_id=35935; lemma=semantika; gloss=semantics); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** standardna semantika: The source itself uses standard as a competing label and the phrase would obscure the all-relations definition.; vseobća semantika: Does not identify the second-order/fullness condition. - **Neizvěstnost / uncertainty:** National literature alternates between full and standard labels; this canon records the definitional reading.; The r0001 record remains preserved as adverse provenance for the target/source locator mismatch. ## OLISV-T0099 · logic.function-symbol - **English lemma / sense:** function symbol — A nonlogical symbol of fixed arity interpreted as a function in a structure. - **Medžuslovjansky:** `funkcijny simbol`; lemma `funkcijny simbol`; masculine noun phrase. - **Upotrěbljenje / inflection:** Genitive funkcijnogo simbola; reserve funkcija for the interpreted mathematical mapping. - **Kirilična forma:** `функцијны симбол` - **Argumentacija / rationale:** The compound preserves the crucial type distinction between an object-language symbol and its interpreted function. - **Uvěrjenost / status:** 0.72 (medium); `provisional`; revision `OLISV-T0099-r0001`. - **Slovjanske sravnenja / comparanda:** ru: функциональный символ; uk: функціональний символ; pl: symbol funkcyjny; cs: funkční symbol; bcs: funkcijski simbol; функцијски симбол; bg: функционален символ. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[7434]; dictionary_id=1289); ISV-DICT-LIVE-20260825 (wordList[16812]; dictionary_id=12221); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** funkcija: The bare word names the interpreted mapping and reproduces the source's metalinguistic conflation. - **Neizvěstnost / uncertainty:** The adjective funkcijny and the complete compound are editorial derivations. ## OLISV-T0318 · logic.fuzzy - **English lemma / sense:** fuzzy logic — A logic designed in the source to model reasoning about vague properties rather than only sharply binary classifications. - **Medžuslovjansky:** `razmyta logika`; lemma `razmyta logika`; feminine participial-adjective noun phrase. - **Upotrěbljenje / inflection:** Feminine logika; genitive razmytoj logiky and plural razmyte logiky. - **Kirilična forma:** `размыта логика` - **Argumentacija / rationale:** Razmyta logika transfers the shared blur metaphor used by several Slavic traditions while retaining the stable logic head. It remains distinct from nejasno svojstvo, so the name of the formalism is not confused with a merely unclear specification. - **Uvěrjenost / status:** 0.82 (high); `provisional`; revision `OLISV-T0318-r0001`. - **Slovjanske sravnenja / comparanda:** ru: нечёткая логика; uk: нечітка логіка; pl: logika rozmyta; cs: fuzzy logika; mlhavá logika; bcs: neizrazita logika; расплинута логика; bg: размита логика. - **Dokazy / evidence:** OL-FOL-BEYOND-OTHER-LOGICS (lines 23-24); ISV-DICT-LIVE-20260825 (dictionary_id=30337; lemma=råzmyti; gloss=blur); ISV-DICT-LIVE-20260825 (dictionary_id=30338; lemma=råzmyvati; gloss=blur); ISV-DICT-LIVE-20260825 (dictionary_id=8933; lemma=logika; gloss=logic); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** nejasna logika: Nejasny directly serves the source's vague property, but calling the logic itself unclear would suggest defective exposition rather than graded truth or membership. - **Neizvěstnost / uncertainty:** National traditions divide between fuzzy loans, sharpness metaphors, and blur metaphors; razmyta is a transparent edition preference rather than native certification. ## OLISV-T0223 · logic.higher-order - **English lemma / sense:** higher-order logic — The family of logical frameworks that allow quantification of higher order, here contrasted with first-order logic and including second-order reasoning. - **Medžuslovjansky:** `logika vyššego reda`; lemma `logika vyššego reda`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive logiky vyššego reda. Use as an umbrella; keep logika drugogo reda for the second-order subtype and logika vyšših tipov for the historically specific type hierarchy. - **Kirilična forma:** `логика вышшего реда` - **Argumentacija / rationale:** The phrase extends the established T0090 genitive order construction and preserves the source's umbrella contrast with first-order logic. It remains distinct from both the second-order subtype and the historically specific higher-type system. The frozen dictionary directly attests vysši; selected vyšši is a disclosed edition-level normalization continuous with the installed translation, not a falsely claimed dictionary form. - **Uvěrjenost / status:** 0.86 (high); `provisional`; revision `OLISV-T0223-r0001`. - **Slovjanske sravnenja / comparanda:** ru: логика высшего порядка; uk: логіка вищого порядку; pl: logika wyższego rzędu; cs: logika vyššího řádu; bcs: logika višeg reda; логика вишег реда; bg: логика от по-висок ред. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[10431]; dictionary_id=8933; lemma=logika; gloss=logic); ISV-DICT-LIVE-20260825 (wordList[8494]; dictionary_id=20302; lemma=vysši; gloss=higher); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** logika vyššego poredka: Several East-Slavic comparanda use the order/poryadok family, but poredȯk would break the edition's established logika prvogo reda construction. - **Neizvěstnost / uncertainty:** Several national traditions use an order lexeme not identical to the canonical red construction.; The frozen row directly attests vysši rather than the selected edition-normalized vyšši surface. ## OLISV-T0225 · logic.higher-type - **English lemma / sense:** higher-type logic — The type-hierarchical logical framework attributed here to Russell and Whitehead's Principia Mathematica, historically distinct from the broader higher-order umbrella. - **Medžuslovjansky:** `logika vyšših tipov`; lemma `logika vyšših tipov`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive logiky vyšših tipov. Keep the plural genitive type complement when referring to the hierarchy. - **Kirilična forma:** `логика вышших типов` - **Argumentacija / rationale:** The transparent international type compound preserves the historically specific description of Principia and prevents its collapse into the broader higher-order label. The frozen dictionary directly attests vysši; selected vyšši is a disclosed edition-level normalization continuous with the installed translation, not a falsely claimed dictionary form. - **Uvěrjenost / status:** 0.84 (high); `provisional`; revision `OLISV-T0225-r0001`. - **Slovjanske sravnenja / comparanda:** ru: логика высших типов; uk: логіка вищих типів; pl: logika wyższych typów; cs: logika vyšších typů; bcs: logika viših tipova; логика виших типова; bg: логика на висшите типове. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[10431]; dictionary_id=8933; lemma=logika; gloss=logic); ISV-DICT-LIVE-20260825 (wordList[8494]; dictionary_id=20302; lemma=vysši; gloss=higher); ISV-DICT-LIVE-20260825 (wordList[17844]; dictionary_id=3224; lemma=tip; gloss=type, kind); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** logika vyššego reda: This broader umbrella loses the source's historically significant type-hierarchy distinction. - **Neizvěstnost / uncertainty:** The source gives a high-level historical characterization and does not specify a particular type-theoretic calculus.; The frozen row directly attests vysši rather than the selected edition-normalized vyšši surface. ## OLISV-T0263 · logic.higher-type-quantification - **English lemma / sense:** higher-type quantification — Quantification over variables whose types may be functions, products, or other higher finite types. - **Medžuslovjansky:** `kvantifikacija nad vyššimi tipami`; lemma `kvantifikacija nad vyššimi tipami`; feminine noun phrase. - **Upotrěbljenje / inflection:** Feminine kvantifikacija; use nad vyššimi tipami with the instrumental plural after nad. Keep vyšši as the normalized higher adjective. - **Kirilična forma:** `квантификација над вышшими типами` - **Argumentacija / rationale:** The source names higher-type quantification as a distinct formula-forming resource. The phrase composes the established kvantifikacija family with the higher/type components and makes the quantifier's range explicit. - **Uvěrjenost / status:** 0.9 (high); `provisional`; revision `OLISV-T0263-r0002`. - **Slovjanske sravnenja / comparanda:** ru: квантификация высших типов; uk: квантифікація над типами вищого порядку; pl: kwantyfikacja wyższych typów; cs: kvantifikace vyšších typů; bcs: kvantifikacija viših tipova; квантификација виших типова; bg: квантификация от висши типове. - **Dokazy / evidence:** OL-FOL-BEYOND-HIGHER-ORDER-LOGIC (lines 87-93); ISV-DICT-LIVE-20260825 (dictionary_id=20302; lemma=vysši; gloss=higher); ISV-DICT-LIVE-20260825 (dictionary_id=3224; lemma=tip; gloss=type, kind); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** kvantifikacija funkcij: Too narrow: variables may range over products and other higher types, not only functions.; vyššorędna kvantifikacija: A compressed calque obscures whether higher modifies order, type, or the quantifier itself. - **Neizvěstnost / uncertainty:** The dictionary row is vysši; the edition's vyšši is a regular normalized surface used by the existing higher-type canon.; The r0001 record is preserved as adverse provenance for the evidence correction. ## OLISV-T0266 · logic.higher-type-semantics - **English lemma / sense:** higher-type semantics — An interpretation framework assigning domains and operations to each finite type. - **Medžuslovjansky:** `semantika vyšših tipov`; lemma `semantika vyšših tipov`; feminine noun phrase. - **Upotrěbljenje / inflection:** Feminine semantika; genitive semantiky vyšših tipov. Use višši only in quoted national comparanda; the edition uses vyšši. - **Kirilična forma:** `семантика вышших типов` - **Argumentacija / rationale:** The source contrasts several versions of semantics for the higher-type system. The phrase composes the already established semantika and higher-type families and serves as the neutral umbrella before full and weak variants are distinguished. - **Uvěrjenost / status:** 0.92 (high); `provisional`; revision `OLISV-T0266-r0002`. - **Slovjanske sravnenja / comparanda:** ru: семантика высших типов; uk: семантика типів вищого порядку; pl: semantyka wyższych typów; cs: sémantika vyšších typů; bcs: semantika viših tipova; семантика виших типова; bg: семантика на висши типове. - **Dokazy / evidence:** OL-FOL-BEYOND-HIGHER-ORDER-LOGIC (lines 102-112); ISV-DICT-LIVE-20260825 (dictionary_id=20302; lemma=vysši; gloss=higher); ISV-DICT-LIVE-20260825 (dictionary_id=3224; lemma=tip; gloss=type, kind); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3); ISV-DICT-LIVE-20260825 (dictionary_id=35935; lemma=semantika; gloss=semantics) - **Alternativy / alternatives:** interpretacija vyšših tipov: Interpretation is a model assignment, not the entire semantic framework distinguished by the source.; semantika funkcij: Too narrow for product and base types. - **Neizvěstnost / uncertainty:** Higher-type terminology is conventionally plural in the genitive; the exact national adjective order varies.; The r0001 record is preserved as adverse provenance for the evidence correction. ## OLISV-T0108 · logic.identity - **English lemma / sense:** identity — The distinguished two-place logical relation expressing that two terms denote the same object. - **Medžuslovjansky:** `identičnost`; lemma `identičnost`; feminine noun. - **Upotrěbljenje / inflection:** Genitive identičnosti; record that many traditions call the same symbol equality. - **Kirilična forma:** `идентичност` - **Argumentacija / rationale:** Standard-Latin normalization of a direct identity lemma with strong international and native comparanda. - **Uvěrjenost / status:** 0.82 (medium); `provisional`; revision `OLISV-T0108-r0001`. - **Slovjanske sravnenja / comparanda:** ru: идентичность, тождество; uk: ідентичність, тотожність; pl: tożsamość; cs: identita; bcs: identičnost, istovjetnost; идентичност, истоветност, једнакост; bg: самоличност, идентичност. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[8849]; dictionary_id=35748); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** ravnost: Equality is an important alternative, but this source explicitly labels the logical symbol identity. - **Neizvěstnost / uncertainty:** The equality/identity naming choice is conventional and must remain visible. ## OLISV-T0148 · logic.immediate-subformula - **English lemma / sense:** immediate subformula — A subformula supplied directly by the outermost constructor of a formula, before recursively including smaller subformulas. - **Medžuslovjansky:** `bezposrědnja podformula`; lemma `bezposrědnja podformula`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive bezposrědnej podformuly; the soft adjective agrees with feminine podformula and distinguishes the immediate relation from the proper-subformula closure. - **Kirilična forma:** `безпосрєдња подформула` - **Argumentacija / rationale:** Bezposrědnja is directly recorded with the senses direct and immediate, and podformula reuses the new specialist head. The compound therefore distinguishes the one-step constructor relation without claiming a dictionary-certified specialist head. - **Uvěrjenost / status:** 0.82 (medium); `provisional`; revision `OLISV-T0148-r0001`. - **Slovjanske sravnenja / comparanda:** ru: непосредственная подформула; uk: безпосередня підформула; pl: bezpośrednia podformuła; cs: bezprostřední podformule; bcs: neposredna podformula; непосредна подформула; bg: непосредствена подформула. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-GRAMMAR-ADJ (lines 14-18); ISV-DICT-LIVE-20260825 (wordList[5262]; dictionary_id=1792); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** neposrědnja podformula: The near-synonym neposrědnja is also dictionary-backed, but bezposrědnja is the better cross-Slavic bridge for the source's immediate/direct contrast and aligns with accepted edition usage. - **Neizvěstnost / uncertainty:** The complete compound is editorial; the dictionary row certifies the adjective, not a native specialist term.; Bezposrědnje can also mean directly; the surrounding definition and the explicit proper-subformula contrast fix the technical sense.; No official or native certification is claimed for the complete specialist compound. ## OLISV-T0129 · logic.implication - **English lemma / sense:** implication — The implication connective, classically truth-functional and constructively interpreted as a proof-transforming procedure; in Kripke semantics it is forced at a world exactly when every later world forcing the antecedent also forces the consequent. - **Medžuslovjansky:** `implikacija`; lemma `implikacija`; feminine noun. - **Upotrěbljenje / inflection:** Genitive implikacije; use semantic consequence slědovanje for the model-theoretic relation. - **Kirilična forma:** `импликација` - **Argumentacija / rationale:** International term converges strongly and remains distinct from canonical semantic consequence. The dedicated OLP-0179 unit now broadens the current sense while the earlier revision remains preserved as scope provenance. - **Uvěrjenost / status:** 0.9 (high); `provisional`; revision `OLISV-T0129-r0002`. - **Slovjanske sravnenja / comparanda:** ru: импликация; uk: імплікація; pl: implikacja; cs: implikace; bcs: implikacija; импликација; bg: импликация. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 97-107 and 217-218); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** slědovanje: Semantic consequence is not the same as the material conditional connective. - **Neizvěstnost / uncertainty:** In informal mathematics implication can also name consequence; the edition keeps the formal distinction explicit.; Earlier narrower sense wording remains preserved in the superseded revision. ## OLISV-T0239 · logic.impredicative - **English lemma / sense:** impredicative — Allowing a definition whose quantifiers range over a totality that includes the object being defined. - **Medžuslovjansky:** `impredikativny`; lemma `impredikativny`; hard adjective. - **Upotrěbljenje / inflection:** Use impredikativna shema (feminine), impredikativno opreděljenje (neuter), and impredikativny sistem (masculine). - **Kirilična forma:** `импредикативны` - **Argumentacija / rationale:** The international mathematical adjective is maximally transparent across the six comparison languages and directly preserves the source's self-inclusion criterion. It is marked derived because the bounded dictionary has no direct headword. - **Uvěrjenost / status:** 0.69 (medium); `provisional`; revision `OLISV-T0239-r0002`. - **Slovjanske sravnenja / comparanda:** ru: импредикативный; uk: імпредикативний; pl: impredykatywny; cs: impredikativní; bcs: impredikativan; импредикативан; bg: импредикативен. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (dictionary_id=20174; lemma=semantičny; gloss=semantic); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** samopredikativny: Suggests self-predication rather than quantification over the totality containing the defined relation.; kružny: Too broad and loses the formal impredicativity criterion. - **Neizvěstnost / uncertainty:** Specialist national spelling and the boundary between impredicative and circular vary by tradition.; The r0001 record remains preserved as adverse provenance for the target/source locator mismatch. ## OLISV-T0103 · logic.inductive-definition - **English lemma / sense:** inductive definition — A definition giving base objects and closure clauses that generate the least admissible class. - **Medžuslovjansky:** `induktivna definicija`; lemma `induktivna definicija`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive induktivnoj definicije; do not infer unique readability without separate parsing conditions. - **Kirilična forma:** `индуктивна дефиниција` - **Argumentacija / rationale:** International components converge throughout the specialist comparison languages. - **Uvěrjenost / status:** 0.86 (high); `provisional`; revision `OLISV-T0103-r0001`. - **Slovjanske sravnenja / comparanda:** ru: индуктивное определение; uk: індуктивне визначення; pl: definicja indukcyjna; cs: induktivní definice; bcs: induktivna definicija; индуктивна дефиниција; bg: индуктивна дефиниция. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[4862]; dictionary_id=2624); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** rekursivna definicija: Recursive definition is related but need not emphasize least-class generation in the same way. - **Neizvěstnost / uncertainty:** The dictionary directly attests definicija but not the complete specialist compound. ## OLISV-T0310 · logic.intensional - **English lemma / sense:** intensional logic — A logic whose semantics ranges over a richer ontology or multiple worlds rather than only the actual world. - **Medžuslovjansky:** `intensionalna logika`; lemma `intensionalna logika`; feminine adjective-noun phrase. - **Upotrěbljenje / inflection:** Feminine logika; genitive intensionalnoj logiky. - **Kirilična forma:** `интенсионална логика` - **Argumentacija / rationale:** Intensionalna logika preserves the source's established international contrast with extensional logic and lets the following ontology explanation carry the specialist sense. No unsupported dictionary claim is made for the full philosophical compound. - **Uvěrjenost / status:** 0.82 (high); `provisional`; revision `OLISV-T0310-r0001`. - **Slovjanske sravnenja / comparanda:** ru: интенсиональная логика; uk: інтенсіональна логіка; pl: logika intensjonalna; cs: intenzionální logika; bcs: intenzionalna logika; bg: интензионална логика. - **Dokazy / evidence:** OL-FOL-BEYOND-MODAL-LOGICS (lines 50-57); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** logika značenja: A meaning-logic paraphrase is too broad and loses continuity with the established intensional/extensional literature pair. - **Neizvěstnost / uncertainty:** Intension/extension terminology is theory-laden and national spellings vary; this is an edition-level international form. ## OLISV-T0269 · logic.intuitionistic - **English lemma / sense:** intuitionistic logic — An intuitionistic logical framework—first-order here, with analogous second- and higher-order versions—obtained by restricting a derivation system for classical first-order logic so as to model constructive reasoning and proof-giving interpretations. - **Medžuslovjansky:** `intuicionistična logika`; lemma `intuicionistična logika`; feminine noun phrase. - **Upotrěbljenje / inflection:** Feminine logika; genitive intuicionističnoj logikě. Keep the international -ističny adjective and the established logika head. - **Kirilična forma:** `интуиционистична логика` - **Argumentacija / rationale:** The target already uses intuicionistična logika, and the source explicitly contrasts its constructive reading with classical logic. The adjective is a regular international derivative of the direct intuicija row and is not presented as an official national spelling. The dedicated OLP-0179 unit now broadens the current sense while the earlier revision remains preserved as scope provenance. - **Uvěrjenost / status:** 0.9 (high); `provisional`; revision `OLISV-T0269-r0003`. - **Slovjanske sravnenja / comparanda:** ru: интуиционистская логика; uk: інтуїціоністська логіка; pl: logika intuicjonistyczna; cs: intuicionistická logika; bcs: intuicionistička logika; интуиционистичка логика; bg: интуиционистка логика. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 13-17 and 74-126); OL-FOL-BEYOND-HIGHER-ORDER-LOGIC (lines 114-123); ISV-DICT-LIVE-20260825 (dictionary_id=8933; lemma=logika; gloss=logic); ISV-DICT-LIVE-20260825 (dictionary_id=6159; lemma=intuicija; gloss=intuition); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** konstruktivna logika: Constructive is a related but broader label; the source specifically names intuitionistic logic before discussing constructive interpretations.; logika intuicije: A genitive phrase suggests psychology rather than the established formal school. - **Neizvěstnost / uncertainty:** The dictionary does not list the full adjective; its international derivation and the source's explicit label support the provisional form.; The r0001 record is preserved as adverse provenance for the evidence correction.; Earlier narrower sense wording remains preserved in the superseded revision. ## OLISV-T0326 · logic.knowledge - **English lemma / sense:** knowledge — The epistemic state that the source identifies as an object of reasoning modeled by epistemic logic. - **Medžuslovjansky:** `znanje`; lemma `znanje`; neuter abstract noun. - **Upotrěbljenje / inflection:** Neuter abstract noun; genitive znanja and locative znanju. - **Kirilična forma:** `знање` - **Argumentacija / rationale:** Znanje is a transparent regular derivative of the pan-Slavic znati base and aligns especially strongly with Ukrainian and South Slavic surfaces. It keeps the abstract epistemic state distinct from acquaintance, expertise, or a collection of facts. - **Uvěrjenost / status:** 0.81 (high); `provisional`; revision `OLISV-T0326-r0001`. - **Slovjanske sravnenja / comparanda:** ru: знание; uk: знання; pl: wiedza; cs: znalost; vědění; bcs: znanje; знање; bg: знание. - **Dokazy / evidence:** OL-FOL-BEYOND-OTHER-LOGICS (lines 28-29); ISV-DICT-LIVE-20260825 (dictionary_id=372; lemma=znati; gloss=know); ISV-DICT-LIVE-20260825 (dictionary_id=14290; lemma=znalosť; gloss=knowledge); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** znalosť: The frozen noun is directly listed but tends toward acquaintance, familiarity, or skill in several languages; znanje is broader and more transparent in this epistemic context. - **Neizvěstnost / uncertainty:** West Slavic readers may prefer a vědění or wiedza family, while the edition prioritizes the wider East/South znanje pattern. ## OLISV-T0294 · logic.kripke-semantics - **English lemma / sense:** Kripke semantics — The semantics for intuitionistic logic based on ordered worlds, persistent valuations, and a forcing relation. - **Medžuslovjansky:** `Kripkova semantika`; lemma `Kripkova semantika`; feminine possessive-adjective noun phrase. - **Upotrěbljenje / inflection:** Feminine semantika; genitive Kripkovoj semantiky. - **Kirilična forma:** `Крипкова семантика` - **Argumentacija / rationale:** Kripkova semantika combines the direct semantic head with a transparent possessive proper-name form; the subsequent ordered-world clauses fix the intuitionistic sense. - **Uvěrjenost / status:** 0.96 (high); `provisional`; revision `OLISV-T0294-r0001`. - **Slovjanske sravnenja / comparanda:** ru: семантика Крипке; uk: семантика Кріпке; pl: semantyka Kripkego; cs: Kripkeho sémantika; bcs: Kripkeova semantika; Крипкеова семантика; bg: семантика на Крипке. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 180-222); ISV-DICT-LIVE-20260825 (dictionary_id=35935; lemma=semantika; gloss=semantics); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** semantika možnyh světov: Possible-world semantics is broader and would hide the source's Kripke attribution and persistence clauses. - **Neizvěstnost / uncertainty:** The indeclinable national treatment of Kripke varies; the possessive adjective is an edition convention. ## OLISV-T0295 · logic.kripke-structure - **English lemma / sense:** Kripke structure — A triple of worlds, a partial order with a least element, and a monotone valuation for a propositional language. - **Medžuslovjansky:** `Kripkova struktura`; lemma `Kripkova struktura`; feminine possessive-adjective noun phrase. - **Upotrěbljenje / inflection:** Feminine struktura; plural Kripkove struktury, genitive Kripkovoj struktury. - **Kirilična forma:** `Крипкова структура` - **Argumentacija / rationale:** Kripkova struktura follows the source's named triple and direct structure head, while the entry definition prevents confusion with arbitrary relational structures. - **Uvěrjenost / status:** 0.97 (high); `provisional`; revision `OLISV-T0295-r0001`. - **Slovjanske sravnenja / comparanda:** ru: структура Крипке; uk: структура Кріпке; pl: struktura Kripkego; cs: Kripkeho struktura; bcs: Kripkeova struktura; Крипкеова структура; bg: структура на Крипке. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 186-222); ISV-DICT-LIVE-20260825 (dictionary_id=16363; lemma=struktura; gloss=structure); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** Kripkov model: Model is common in the literature but would erase the source's explicit structure terminology and collide with the broader model canon. - **Neizvěstnost / uncertainty:** Some literature prefers Kripke model or frame; this entry follows the pinned source's structure label. ## OLISV-T0297 · logic.kripke-world - **English lemma / sense:** Kripke world — An element of the ordered set in a Kripke structure, interpreted as a state of knowledge. - **Medžuslovjansky:** `Kripkov svět`; lemma `Kripkov svět`; masculine possessive-adjective noun phrase. - **Upotrěbljenje / inflection:** Masculine svět; plural Kripkove světy, genitive Kripkovogo světa. - **Kirilična forma:** `Крипков свєт` - **Argumentacija / rationale:** Kripkov svět uses the direct world head and keeps the source's state-of-knowledge explanation in the definition rather than replacing the conventional world label. - **Uvěrjenost / status:** 0.94 (high); `provisional`; revision `OLISV-T0297-r0001`. - **Slovjanske sravnenja / comparanda:** ru: мир Крипке; uk: світ Кріпке; pl: świat Kripkego; cs: Kripkeho svět; bcs: Kripkeov svijet; Крипкеов свет; bg: свят на Крипке. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 200-210); ISV-DICT-LIVE-20260825 (dictionary_id=3137; lemma=svět; gloss=world); ISV-DICT-LIVE-20260825 (dictionary_id=16479; lemma=stańje; gloss=state (condition, shape), status); ISV-DICT-LIVE-20260825 (dictionary_id=3712; lemma=znańje; gloss=knowledge, know-how); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** stanje znanja: This is the source's interpretation of a world, not the structural element's canonical name. - **Neizvěstnost / uncertainty:** World is metaphorical and some national accounts prefer node or state; the source explicitly licenses both world and state readings. ## OLISV-T0262 · logic.lambda-term - **English lemma / sense:** lambda term — A term formed by abstraction, written with a lambda binder and denoting a function. - **Medžuslovjansky:** `lambda-term`; lemma `lambda-term`; masculine noun phrase. - **Upotrěbljenje / inflection:** Use lambda-term, plural lambda-termy; retain lambda as an international technical symbol and decline term regularly. - **Kirilična forma:** `ламбда-терм` - **Argumentacija / rationale:** The source introduces lambda abstraction as a term-forming operation. The international lambda-term compound is maximally searchable across logic literature, while the direct term/izraz rows support its grammatical head without pretending that lambda is an ordinary lexical lemma. - **Uvěrjenost / status:** 0.84 (high); `provisional`; revision `OLISV-T0262-r0002`. - **Slovjanske sravnenja / comparanda:** ru: лямбда-терм; uk: лямбда-терм; pl: term lambda; cs: lambda-term; bcs: lambda-term; ламбда-терм; bg: ламбда-терм. - **Dokazy / evidence:** OL-FOL-BEYOND-HIGHER-ORDER-LOGIC (lines 67-68 and 82-89); ISV-DICT-LIVE-20260825 (dictionary_id=8115; lemma=izraz; gloss=term, phrase, expression); ISV-DICT-LIVE-20260825 (dictionary_id=2091; lemma=termin; gloss=term (phrase)); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** lambda-izraz: Izraz is broad and can suggest any expression, weakening the source's typed-term status.; abstraktna funkcija: Names the denotation rather than the syntactic term. - **Neizvěstnost / uncertainty:** Lambda is retained as an international symbol; no direct Interslavic dictionary head for the compound is claimed.; The r0001 record is preserved as adverse provenance for the evidence correction. ## OLISV-T0097 · logic.logical-connective - **English lemma / sense:** logical connective — A logical operator that combines one or more formulas into a formula. - **Medžuslovjansky:** `logičny sveznik`; lemma `logičny sveznik`; masculine noun phrase. - **Upotrěbljenje / inflection:** Genitive logičnogo sveznika; standard-Latin sveznik normalizes dictionary svęznik. - **Kirilična forma:** `логичны свезник` - **Argumentacija / rationale:** Sveznik is a transparent standardized form of the direct conjunction lemma and avoids the narrower relation sense of vęzka. - **Uvěrjenost / status:** 0.76 (medium); `provisional`; revision `OLISV-T0097-r0001`. - **Slovjanske sravnenja / comparanda:** ru: логическая связка; uk: логічна зв'язка; pl: spójnik logiczny; cs: logická spojka; bcs: logički veznik; логички везник; bg: логическа свързка. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[4001]; dictionary_id=36359); ISV-DICT-LIVE-20260825 (wordList[10432]; dictionary_id=363); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** logična vęzka: Vęzka denotes a bond or relation and is less direct as the grammatical/logical combining category. - **Neizvěstnost / uncertainty:** The frozen dictionary directly attests only the grammatical conjunction sense, not the complete logical compound.; Earlier translated units contain veznik and vęzka variants; this entry governs future normalization without rewriting history. ## OLISV-T0122 · logic.logical-symbol - **English lemma / sense:** logical symbol — A symbol whose interpretation or inferential role is fixed by the logical system. - **Medžuslovjansky:** `logičny simbol`; lemma `logičny simbol`; masculine noun phrase. - **Upotrěbljenje / inflection:** Genitive logičnogo simbola; contrast with nelogičny simbol. - **Kirilična forma:** `логичны симбол` - **Argumentacija / rationale:** Both components are directly attested and the compound converges across all national traditions. - **Uvěrjenost / status:** 0.9 (high); `provisional`; revision `OLISV-T0122-r0001`. - **Slovjanske sravnenja / comparanda:** ru: логический символ; uk: логічний символ; pl: symbol logiczny; cs: logický symbol; bcs: logički simbol; логички симбол; bg: логически символ. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[10432]; dictionary_id=363); ISV-DICT-LIVE-20260825 (wordList[16812]; dictionary_id=12221); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** formalny simbol: Formal is broader and does not mark the logical/nonlogical division. - **Neizvěstnost / uncertainty:** Which symbols count as logical is a convention of the formal system. ## OLISV-T0222 · logic.logical-system - **English lemma / sense:** logical system — A system treated as a logic, typically involving a formally specified language and usually—but not invariably—a derivation system and intended semantics. These are defeasible characteristics in this source, not necessary-and-sufficient component requirements. - **Medžuslovjansky:** `logičny sistem`; lemma `logičny sistem`; masculine adjective-noun phrase. - **Upotrěbljenje / inflection:** Genitive logičnogo sistema; nominative plural logične sistemy. Keep logika for the discipline or contextually individuated logic. - **Kirilična forma:** `логичны систем` - **Argumentacija / rationale:** The source now gives a defeasible profile rather than a definition: formal language specification is typical, and a derivation system and intended semantics are each usual but expressly not invariant. The adjective is directly frozen and pan-Slavically convergent; masculine sistem remains the established edition form while dictionary feminine sistema stays visible as adverse evidence. - **Uvěrjenost / status:** 0.9 (high); `provisional`; revision `OLISV-T0222-r0002`. - **Slovjanske sravnenja / comparanda:** ru: логическая система; uk: логічна система; pl: system logiczny; cs: logický systém; bcs: logički sistem; логички систем; bg: логическа система. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[10432]; dictionary_id=363; lemma=logičny; gloss=logical); ISV-DICT-LIVE-20260825 (wordList[16844]; dictionary_id=1317; lemma=sistema; gloss=system); OL-FOL-INTRO-SOUNDNESS-COMPLETENESS-ISV (lines 11-25); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** logična sistema: The frozen dictionary directly prefers sistema and several national traditions use a feminine noun, but the accepted edition already fixes masculine sistem in formal-logic compounds; changing gender here would split one project head.; logika: Logika remains necessary as the discipline and can contextually denote an individuated logic, but the source's explicit logical-system phrase deserves a distinct machine-searchable head. - **Neizvěstnost / uncertainty:** The frozen dictionary directly prefers feminine sistema while the accepted edition uses masculine sistem; the latter is retained for internal continuity.; The source's component profile is explicitly defeasible and must not be hardened into a universal definition of logical systems. ## OLISV-T0141 · logic.main-operator - **English lemma / sense:** main operator — The outermost connective or quantifier occurrence that determines a compound formula's immediate syntactic construction. - **Medžuslovjansky:** `glavny operator`; lemma `glavny operator`; masculine noun phrase. - **Upotrěbljenje / inflection:** Genitive glavnogo operatora; the operator is an occurrence in the written formula, not merely an operator type. - **Kirilična forma:** `главны оператор` - **Argumentacija / rationale:** The direct main adjective plus the already canonical operator head names every eligible connective or quantifier without narrowing the category. - **Uvěrjenost / status:** 0.9 (high); `provisional`; revision `OLISV-T0141-r0001`. - **Slovjanske sravnenja / comparanda:** ru: главный оператор; uk: головний оператор; pl: główny operator; cs: hlavní operátor; bcs: glavni operator; главни оператор; bg: главен оператор. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[10634]; dictionary_id=2671); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** glavny sveznik: A connective cannot cover quantified formulas, so the alternative is too narrow for the source theorem. - **Neizvěstnost / uncertainty:** The exact compound is editorial; the dictionary head glåvny is normalized to standard/basic Latin glavny. ## OLISV-T0231 · logic.many-sorted - **English lemma / sense:** many-sorted logic — A logical framework with multiple sorts, each carrying its own variables, quantifiers, and ordinarily identity, while functions and relations have sort profiles. - **Medžuslovjansky:** `mnogosortna logika`; lemma `mnogosortna logika`; feminine adjective-noun phrase. - **Upotrěbljenje / inflection:** Genitive mnogosortnoj logiky; the adjective agrees with feminine logika. - **Kirilična forma:** `многосортна логика` - **Argumentacija / rationale:** The transparent compound preserves the source distinction between several sorts and a separate type profile. - **Uvěrjenost / status:** 0.88 (high); `provisional`; revision `OLISV-T0231-r0001`. - **Slovjanske sravnenja / comparanda:** ru: многосортная логика; uk: багатосортна логіка; pl: logika wielosortowa; cs: vícesortová logika; bcs: mnogosortna logika; многосортна логика; bg: многосортна логика. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[9858]; dictionary_id=3223; lemma=sort; gloss=kind, sort); ISV-DICT-LIVE-20260825 (wordList[11416]; dictionary_id=17077; lemma=mnogy; gloss=much, many, numerous); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** mnogotipna logika: Collapses the source distinction between sorts and typing.; mnogorodna logika: Rod is broader and more polysemous than direct sort. - **Neizvěstnost / uncertainty:** The complete phrase is editorially normalized from pinned components, not a frozen dictionary headword. ## OLISV-T0128 · logic.material-equivalence - **English lemma / sense:** material equivalence — The truth-functional equivalence relation represented by a biconditional. - **Medžuslovjansky:** `materialna ekvivalentnost`; lemma `materialna ekvivalentnost`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive materialnoj ekvivalentnosti; do not conflate with arbitrary mathematical equivalence relations. - **Kirilična forma:** `материална еквивалентност` - **Argumentacija / rationale:** International components are stable across the national logical traditions and the material modifier fixes the intended sense. - **Uvěrjenost / status:** 0.83 (medium); `provisional`; revision `OLISV-T0128-r0001`. - **Slovjanske sravnenja / comparanda:** ru: материальная эквиваленция; uk: матеріальна еквівалентність; pl: równoważność materialna; cs: materiální ekvivalence; bcs: materijalna ekvivalencija; материјална еквиваленција; bg: материална еквивалентност. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** odnošenje ekvivalentnosti: The existing mathematical relation term is broader and does not specify truth-functional material equivalence. - **Neizvěstnost / uncertainty:** Some textbooks use logical equivalence for a semantic relation holding under every valuation rather than the object-language connective. ## OLISV-T0331 · logic.mathematical - **English lemma / sense:** mathematical logic — The mathematical study of formal logical systems, listed by the source as one rubric under which the introduced systems may be studied. - **Medžuslovjansky:** `matematična logika`; lemma `matematična logika`; feminine adjective-noun phrase. - **Upotrěbljenje / inflection:** Feminine logika; genitive matematičnoj logiky. - **Kirilična forma:** `математична логика` - **Argumentacija / rationale:** Matematična logika is a direct, transparent composition whose six-language counterparts are virtually uniform. The source distinguishes the disciplinary rubric from mathematical motivation, and the translation preserves both adjective uses. - **Uvěrjenost / status:** 0.98 (high); `provisional`; revision `OLISV-T0331-r0001`. - **Slovjanske sravnenja / comparanda:** ru: математическая логика; uk: математична логіка; pl: logika matematyczna; cs: matematická logika; bcs: matematička logika; математичка логика; bg: математическа логика. - **Dokazy / evidence:** OL-FOL-BEYOND-OTHER-LOGICS (lines 33-36); ISV-DICT-LIVE-20260825 (dictionary_id=36602; lemma=matematičny; gloss=mathematical); ISV-DICT-LIVE-20260825 (dictionary_id=8933; lemma=logika; gloss=logic); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** logika matematiky: A genitive phrase can mean the logic internal to mathematics rather than the established discipline of mathematical logic. - **Neizvěstnost / uncertainty:** The source does not define the disciplinary boundary; this entry preserves its broad rubric without attempting a narrower taxonomy. ## OLISV-T0151 · logic.minimal-formation-sequence - **English lemma / sense:** minimal formation sequence — A formation sequence having the least possible length for its target formula or term; the minimizing sequence need not be unique. - **Medžuslovjansky:** `minimalna poslědovnost formovanja`; lemma `minimalna poslědovnost formovanja`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive minimalnoj poslědovnosti formovanja; do not imply uniqueness, because distinct minimizing orders may contain the same strings. - **Kirilična forma:** `минимална послєдовност формовања` - **Argumentacija / rationale:** Minimalna retains the source's formal minimization label, agrees with the feminine formation-sequence head, and is directly supported across all frozen comparison columns. The definition and following qualification preserve the distinction between least length and uniqueness. - **Uvěrjenost / status:** 0.86 (high); `provisional`; revision `OLISV-T0151-r0001`. - **Slovjanske sravnenja / comparanda:** ru: минимальная последовательность образования; uk: мінімальна послідовність побудови; pl: minimalny ciąg tworzenia; cs: minimální posloupnost tvorby; bcs: minimalni niz tvorbe; минимални низ творбе; bg: минимална последователност на образуване. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-DICT-LIVE-20260825 (wordList[11107]; dictionary_id=2916); ISV-DICT-LIVE-20260825 (wordList[7252]; dictionary_id=25511); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** najkratša poslědovnost formovanja: The paraphrase is extensionally close but replaces the source's named minimality notion and obscures continuity with standard mathematical minimal terminology. - **Neizvěstnost / uncertainty:** Multiple minimal sequences may exist; the head denotes minimal length, not a unique normal form.; The complete specialist compound is compositional rather than directly dictionary-attested.; No official or native certification is claimed for the complete specialist compound. ## OLISV-T0300 · logic.modal - **English lemma / sense:** modal logic — A logical system extending propositional or predicate logic with operators for necessity and possibility across possible worlds. - **Medžuslovjansky:** `modalna logika`; lemma `modalna logika`; feminine adjective-noun phrase. - **Upotrěbljenje / inflection:** Feminine logika; genitive modalnoj logiky. - **Kirilična forma:** `модална логика` - **Argumentacija / rationale:** Modalna logika combines the directly attested modal adjective with the stable logic head and keeps the source's necessity/possibility distinction visible. The definition, rather than the international label alone, fixes the specialist sense. - **Uvěrjenost / status:** 0.94 (high); `provisional`; revision `OLISV-T0300-r0001`. - **Slovjanske sravnenja / comparanda:** ru: модальная логика; uk: модальна логіка; pl: logika modalna; cs: modální logika; bcs: modalna logika; модална логика; bg: модална логика. - **Dokazy / evidence:** OL-FOL-BEYOND-MODAL-LOGICS (lines 31-39 and 67-89); ISV-DICT-LIVE-20260825 (dictionary_id=37338; lemma=modaľny; gloss=modal); ISV-DICT-LIVE-20260825 (dictionary_id=8933; lemma=logika; gloss=logic); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** logika možlivyh světov: A descriptive possible-worlds phrase explains one semantic device but does not name the broader system, which also applies to predicate logic and alternative modal readings. - **Neizvěstnost / uncertainty:** The dictionary's modal adjective is marked with a soft-l variant while the edition uses the internationally transparent modalna surface; no official specialist certification is claimed. ## OLISV-T0296 · logic.monotone-valuation - **English lemma / sense:** monotone valuation — An assignment of propositional variables that persists upward along the Kripke order. - **Medžuslovjansky:** `monotonna ocěnka`; lemma `monotonna ocěnka`; feminine adjective-noun phrase. - **Upotrěbljenje / inflection:** Feminine ocěnka; plural monotonne ocěnky, genitive monotonnoj ocěnky. - **Kirilična forma:** `монотонна оцєнка` - **Argumentacija / rationale:** Monotonna ocěnka pairs the direct valuation head with the source's quoted monotone qualifier; the future-world clauses explain persistence rather than relying on the everyday monotone sense. - **Uvěrjenost / status:** 0.86 (high); `provisional`; revision `OLISV-T0296-r0001`. - **Slovjanske sravnenja / comparanda:** ru: монотонная оценка; uk: монотонна оцінка; pl: wartościowanie monotoniczne; cs: monotónní ohodnocení; bcs: monotona valuacija; монотоно вредновање; bg: монотонна оценка. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 200-218); ISV-DICT-LIVE-20260825 (dictionary_id=29019; lemma=ocěnka; gloss=mark, rating, score, valuation, estimation, assessment, appraisal, evaluation); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** postojanna ocěnka: Constant valuation would forbid legitimate growth of knowledge and is stronger than monotonicity. - **Neizvěstnost / uncertainty:** The complete adjective-noun compound is not directly listed, and national texts vary between valuation, assignment, and evaluation heads. ## OLISV-T0314 · logic.necessitation-rule - **English lemma / sense:** necessitation rule — The rule allowing one to infer Box A from A in the modal proof system described by the source. - **Medžuslovjansky:** `pravilo neobhodnosti`; lemma `pravilo neobhodnosti`; neuter noun phrase. - **Upotrěbljenje / inflection:** Neuter pravilo; genitive pravila neobhodnosti. The rule is quoted as iz A zaključite Box A. - **Kirilična forma:** `правило необходности` - **Argumentacija / rationale:** Pravilo neobhodnosti names the exact inference displayed in the source and keeps its semantic purpose explicit. The formal quotation remains unchanged, so readers can distinguish the rule name from the rule's notation. - **Uvěrjenost / status:** 0.92 (high); `provisional`; revision `OLISV-T0314-r0001`. - **Slovjanske sravnenja / comparanda:** ru: правило необходимости; uk: правило необхідності; pl: reguła konieczności; cs: pravidlo nutnosti; bcs: pravilo nužnosti; bg: правило за необходимост. - **Dokazy / evidence:** OL-FOL-BEYOND-MODAL-LOGICS (lines 67-77); ISV-DICT-LIVE-20260825 (dictionary_id=3087; lemma=pravilo; gloss=rule); ISV-DICT-LIVE-20260825 (dictionary_id=33109; lemma=neobhodimosť; gloss=necessity); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** pravilo operatora: The operator-only label does not say what inference is licensed and could refer to introduction or elimination rules more generally. - **Neizvěstnost / uncertainty:** Different proof calculi impose side conditions on necessitation; this entry records the rule as stated in the bounded source, not every calculus variant. ## OLISV-T0304 · logic.necessity - **English lemma / sense:** necessity — The modal status expressed by Box A: truth in every relevant possible world, or the corresponding logical notion in S5. - **Medžuslovjansky:** `neobhodnost`; lemma `neobhodnost`; feminine noun. - **Upotrěbljenje / inflection:** Feminine neobhodnost; genitive neobhodnosti. Use neobhodno as the neuter predicative adverb/adjective surface. - **Kirilična forma:** `необходност` - **Argumentacija / rationale:** Neobhodnost follows the direct necessity family and cleanly distinguishes the modal status from mere truth in one world. The source's Box explanation and S5 characterization provide the specialist boundary. - **Uvěrjenost / status:** 0.95 (high); `provisional`; revision `OLISV-T0304-r0001`. - **Slovjanske sravnenja / comparanda:** ru: необходимость; uk: необхідність; pl: konieczność; cs: nutnost; bcs: nužnost; bg: необходимост. - **Dokazy / evidence:** OL-FOL-BEYOND-MODAL-LOGICS (lines 28-35 and 79-81); ISV-DICT-LIVE-20260825 (dictionary_id=33109; lemma=neobhodimosť; gloss=necessity, indispensability); ISV-DICT-LIVE-20260825 (dictionary_id=33105; lemma=neobhodimy; gloss=necessary, essential); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** nujnost: The short South-Slavic-oriented form is possible, but neobhodnost is directly evidenced and remains immediately recognizable in East and West Slavic contexts. - **Neizvěstnost / uncertainty:** National mathematical registers divide between neobhodnost, konieczność, nutnost, and nužnost; no single national form is treated as authoritative. ## OLISV-T0113 · logic.negation - **English lemma / sense:** negation — The unary truth-functional connective reversing truth and falsity. - **Medžuslovjansky:** `negacija`; lemma `negacija`; feminine noun. - **Upotrěbljenje / inflection:** Genitive negacije; the connective itself may also be read as ne. - **Kirilična forma:** `негација` - **Argumentacija / rationale:** International form is stable across the Slavic logical traditions. - **Uvěrjenost / status:** 0.85 (high); `provisional`; revision `OLISV-T0113-r0001`. - **Slovjanske sravnenja / comparanda:** ru: отрицание; uk: заперечення; pl: negacja; cs: negace; bcs: negacija; негација; bg: отрицание. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** odrěčenje: A native-looking alternative is not broadly established for the truth-functional connective. - **Neizvěstnost / uncertainty:** No exact frozen dictionary row attests the logical noun. ## OLISV-T0293 · logic.nonlogical-axiom - **English lemma / sense:** nonlogical axiom — An axiom expressing mathematical subject matter rather than belonging to pure logical calculus. - **Medžuslovjansky:** `nelogična aksioma`; lemma `nelogična aksioma`; feminine adjective-noun phrase. - **Upotrěbljenje / inflection:** Feminine aksioma; plural nelogične aksiomy, genitive nelogičnoj aksiomy. - **Kirilična forma:** `нелогична аксиома` - **Argumentacija / rationale:** Nelogična aksioma follows the source and established specialist opposition to pure logic, but the canon explicitly records that the direct ordinary gloss is illogical, not domain-nonlogical. - **Uvěrjenost / status:** 0.8 (medium); `provisional`; revision `OLISV-T0293-r0001`. - **Slovjanske sravnenja / comparanda:** ru: нелогическая аксиома; uk: нелогічна аксіома; pl: aksjomat pozalogiczny; cs: nelogický axiom; bcs: nelogički aksiom; нелогички аксиом; bg: нелогическа аксиома. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 166-178); ISV-DICT-LIVE-20260825 (dictionary_id=24180; lemma=aksioma; gloss=axiom); ISV-DICT-LIVE-20260825 (dictionary_id=8933; lemma=logika; gloss=logic); ISV-DICT-LIVE-20260825 (dictionary_id=19891; lemma=nelogičny; gloss=illogical); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** iracionalna aksioma: Would mean unreasonable or irrational and would destroy the source's logical-versus-mathematical scope distinction. - **Neizvěstnost / uncertainty:** Outside specialist context nelogičny means illogical; readers should retain the definition and pure-logic contrast. ## OLISV-T0105 · logic.nonlogical-symbol - **English lemma / sense:** nonlogical symbol — A symbol whose interpretation may vary between structures rather than being fixed by the logical system. - **Medžuslovjansky:** `nelogičny simbol`; lemma `nelogičny simbol`; masculine noun phrase. - **Upotrěbljenje / inflection:** Genitive nelogičnogo simbola; includes predicate, constant, and function symbols in this source convention. - **Kirilična forma:** `нелогичны симбол` - **Argumentacija / rationale:** Transparent negated adjective plus a directly attested symbol head matches all comparison traditions. - **Uvěrjenost / status:** 0.83 (medium); `provisional`; revision `OLISV-T0105-r0001`. - **Slovjanske sravnenja / comparanda:** ru: нелогический символ; uk: нелогічний символ; pl: symbol pozalogiczny; cs: nelogický symbol; bcs: nelogički simbol; нелогички симбол; bg: нелогически символ. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[10432]; dictionary_id=363); ISV-DICT-LIVE-20260825 (wordList[16812]; dictionary_id=12221); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** opisny simbol: The alternative does not express the interpretation-varying logical boundary. - **Neizvěstnost / uncertainty:** The exact boundary between logical and nonlogical vocabulary is conventional and system-dependent. ## OLISV-T0323 · logic.nonmonotonic - **English lemma / sense:** nonmonotonic logic — A logic in which adding information can invalidate a previously licensed inference, as explained by the source's overturning clause. - **Medžuslovjansky:** `nemonotonna logika`; lemma `nemonotonna logika`; feminine adjective-noun phrase. - **Upotrěbljenje / inflection:** Feminine logika; genitive nemonotonnoj logiky and plural nemonotonne logiky. - **Kirilična forma:** `немонотонна логика` - **Argumentacija / rationale:** Nemonotonna logika keeps the internationally stable mathematical adjective and applies the regular Interslavic ne- negation. The source's new-information clause protects the term from the everyday sense of monotonous or repetitive. - **Uvěrjenost / status:** 0.9 (high); `provisional`; revision `OLISV-T0323-r0001`. - **Slovjanske sravnenja / comparanda:** ru: немонотонная логика; uk: немонотонна логіка; pl: logika niemonotoniczna; cs: nemonotónní logika; bcs: nemonotona logika; немонотона логика; bg: немонотонна логика. - **Dokazy / evidence:** OL-FOL-BEYOND-OTHER-LOGICS (lines 25-28); ISV-DICT-LIVE-20260825 (dictionary_id=8933; lemma=logika; gloss=logic); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** nepostojanna logika: Nonconstant or unstable logic is not the source concept; nonmonotonicity concerns loss of inferences under premise expansion. - **Neizvěstnost / uncertainty:** The frozen general dictionary does not directly list the mathematical monotonicity adjective; the source and prior edition use supply the technical boundary. ## OLISV-T0111 · logic.notation - **English lemma / sense:** notation — A conventional system for writing formal expressions and operators. - **Medžuslovjansky:** `notacija`; lemma `notacija`; feminine noun. - **Upotrěbljenje / inflection:** Genitive notacije; use zapis for a particular written occurrence rather than the system. - **Kirilična forma:** `нотација` - **Argumentacija / rationale:** Direct international lemma with broad cross-Slavic convergence. - **Uvěrjenost / status:** 0.92 (high); `provisional`; revision `OLISV-T0111-r0001`. - **Slovjanske sravnenja / comparanda:** ru: нотация, запись; uk: нотація, запис; pl: notacja, zapis; cs: notace, zápis; bcs: notacija, bilježenje, označivanje; нотација; bg: нотация. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[11842]; dictionary_id=36115); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** zapis: Zapis is directly attested but more readily names an individual inscription or record. - **Neizvěstnost / uncertainty:** The dictionary also offers zapis; the use note preserves the distinction. ## OLISV-T0330 · logic.obligation - **English lemma / sense:** obligation — A moral or ethical requirement whose logical treatment motivates the deontic systems named by the source. - **Medžuslovjansky:** `obvęzȯk`; lemma `obvęzȯk`; masculine noun. - **Upotrěbljenje / inflection:** Masculine noun; genitive obvęzka and contextual locative plural obvęzkah. - **Kirilična forma:** `обвезок` - **Argumentacija / rationale:** Obvęzȯk is the direct frozen obligation head and its national columns cover duty, obligation, and commitment. The source's paired moral and ethical adjectives narrow that broad lexical field to the deontic requirement sense. - **Uvěrjenost / status:** 0.95 (high); `provisional`; revision `OLISV-T0330-r0001`. - **Slovjanske sravnenja / comparanda:** ru: обязанность; обязательство; uk: обов'язок; зобов'язання; pl: obowiązek; zobowiązanie; cs: povinnost; závazek; bcs: obveza; обавеза; bg: задължение; дълг. - **Dokazy / evidence:** OL-FOL-BEYOND-OTHER-LOGICS (lines 31-32); ISV-DICT-LIVE-20260825 (dictionary_id=95; lemma=obvęzȯk; gloss=duty, obligation, commitment); ISV-DICT-LIVE-20260825 (dictionary_id=32285; lemma=moraľny; gloss=moral); ISV-DICT-LIVE-20260825 (dictionary_id=23545; lemma=etičny; gloss=ethical); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** dolžnost: A duty-family alternative is recognizable but can also denote an office or position; the direct obvęzȯk entry better covers the source's obligation sense. - **Neizvěstnost / uncertainty:** The lemma spans duty, obligation, and commitment; the source context, not the bare word, fixes the logical reading. ## OLISV-T0136 · logic.opening-parenthesis - **English lemma / sense:** opening parenthesis — The left member of a parenthesis pair that begins a grouped expression. - **Medžuslovjansky:** `otvarjajuća zatvorka`; lemma `otvarjajuća zatvorka`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive otvarjajućej zatvorky; pair with zatvarjajuća zatvorka. - **Kirilična forma:** `отварјајуча затворка` - **Argumentacija / rationale:** Direct open and parenthesis components yield a transparent form matching every comparison language's directional distinction. - **Uvěrjenost / status:** 0.9 (high); `provisional`; revision `OLISV-T0136-r0001`. - **Slovjanske sravnenja / comparanda:** ru: открывающая скобка; uk: відкривна дужка; pl: nawias otwierający; cs: otevírací závorka; bcs: otvarajuća zagrada; отварајућа заграда; bg: отваряща скоба. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[12120]; dictionary_id=2399); ISV-DICT-LIVE-20260825 (wordList[2433]; dictionary_id=35498); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** lěva zatvorka: Left is visually clear but less robust across writing-direction contexts and does not name the opening function. - **Neizvěstnost / uncertainty:** The participial compound is compositional rather than a direct row. ## OLISV-T0123 · logic.operator - **English lemma / sense:** operator — A formal operation symbol, here covering connectives and quantifiers when treated uniformly. - **Medžuslovjansky:** `operator`; lemma `operator`; masculine noun. - **Upotrěbljenje / inflection:** Genitive operatora; use the narrower sveznik or kvantifikator when the class matters. - **Kirilična forma:** `оператор` - **Argumentacija / rationale:** International specialist noun is universally recognizable and already embedded in source terminology. - **Uvěrjenost / status:** 0.85 (high); `provisional`; revision `OLISV-T0123-r0001`. - **Slovjanske sravnenja / comparanda:** ru: оператор; uk: оператор; pl: operator; cs: operátor; bcs: operator; оператор; bg: оператор. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** operacija: The operation is the semantic or syntactic action, not necessarily the symbol that performs it. - **Neizvěstnost / uncertainty:** The dictionary contains only an operator-derived adjective, not the mathematical/logical noun. ## OLISV-T0182 · logic.parallel-postulate - **English lemma / sense:** parallel postulate — The geometric postulate used as the source's standard example of an axiom independent of the remaining axioms of a theory. - **Medžuslovjansky:** `paralelny postulat`; lemma `paralelny postulat`; masculine noun phrase. - **Upotrěbljenje / inflection:** Postulat is masculine; paralelny agrees regularly. Use genitive paralelnogo postulata. - **Kirilična forma:** `паралелны постулат` - **Argumentacija / rationale:** Paralelny postulat combines two directly frozen international components and maximizes recognition in East and South Slavic languages. Polish and Czech native parallel-family forms remain visible adverse evidence rather than being silently normalized away. - **Uvěrjenost / status:** 0.9 (high); `provisional`; revision `OLISV-T0182-r0001`. - **Slovjanske sravnenja / comparanda:** ru: постулат параллельности; uk: постулат паралельності; pl: postulat równoległości; cs: postulát rovnoběžnosti; bcs: postulat paralelnosti; bg: постулат за успоредността. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[13219]; dictionary_id=36464; lemma=postulat; gloss=postulate); ISV-DICT-LIVE-20260825 (wordList[12435-12437]; dictionary_id=23205,23206,23207; lemma=råvnoběžny,paralela,paraleľny; gloss=parallel); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** råvnoběžny postulat: Råvnoběžny is directly listed and especially transparent in Polish and Czech, but the international paralel- family has broader direct reach in Russian, Ukrainian, South Slavic, Macedonian, and Bulgarian. - **Neizvěstnost / uncertainty:** Polish and Czech favor native parallel-family terminology even though the international selected phrase remains transparent. ## OLISV-T0125 · logic.parenthesis - **English lemma / sense:** parenthesis — A punctuation symbol used to delimit the syntactic grouping of an expression. - **Medžuslovjansky:** `zatvorka`; lemma `zatvorka`; feminine noun. - **Upotrěbljenje / inflection:** Genitive zatvorky; use the plural zatvorky for a matching pair. - **Kirilična forma:** `затворка` - **Argumentacija / rationale:** Direct bracket/parenthesis lemma bridges East, West, and South national terms through a transparent closure root. - **Uvěrjenost / status:** 0.86 (high); `provisional`; revision `OLISV-T0125-r0001`. - **Slovjanske sravnenja / comparanda:** ru: скобка (знак препинания); uk: дужка (розділовий знак), дужка; pl: nawias; cs: závorka; bcs: zagrada; заграда; bg: скоба. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[2433]; dictionary_id=35498); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** skobka: The East-Slavic loan is familiar but substantially less accessible in West and South Slavic. - **Neizvěstnost / uncertainty:** The lemma covers brackets generally; the source restricts it to grouping parentheses. ## OLISV-T0332 · logic.philosophical - **English lemma / sense:** philosophical logic — The philosophically motivated study of logical systems, listed by the source as a disciplinary rubric distinct from mathematical logic. - **Medžuslovjansky:** `filozofska logika`; lemma `filozofska logika`; feminine adjective-noun phrase. - **Upotrěbljenje / inflection:** Feminine logika; genitive filozofskoj logiky. - **Kirilična forma:** `филозофска логика` - **Argumentacija / rationale:** Filozofska logika directly uses the frozen philosophical adjective and stable logic head, avoiding an unnecessary derived filosofi- form. It preserves both the source's motivation adjective and its disciplinary rubric. - **Uvěrjenost / status:** 0.96 (high); `provisional`; revision `OLISV-T0332-r0001`. - **Slovjanske sravnenja / comparanda:** ru: философская логика; uk: філософська логіка; pl: logika filozoficzna; cs: filozofická logika; bcs: filozofska logika; филозофска логика; bg: философска логика. - **Dokazy / evidence:** OL-FOL-BEYOND-OTHER-LOGICS (lines 33-36); ISV-DICT-LIVE-20260825 (dictionary_id=36442; lemma=filozofsky; gloss=philosophical); ISV-DICT-LIVE-20260825 (dictionary_id=8933; lemma=logika; gloss=logic); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** filosofična logika: This earlier-looking derivative is understandable but diverges from the direct frozen filozofsky head and the strongest South/West Slavic correspondences. - **Neizvěstnost / uncertainty:** Russian and Bulgarian retain an s spelling where several other languages use z; the Interslavic dictionary's filozofsky surface governs this edition choice. ## OLISV-T0112 · logic.polish-notation - **English lemma / sense:** Polish notation — Prefix notation in which operators precede their operands and parentheses can be omitted. - **Medžuslovjansky:** `poljska notacija`; lemma `poljska notacija`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive poljskoj notacije; capitalize only when normal title conventions require it. - **Kirilična forma:** `пољска нотација` - **Argumentacija / rationale:** Transparent compound of two directly attested components and standard specialist national forms. - **Uvěrjenost / status:** 0.88 (high); `provisional`; revision `OLISV-T0112-r0001`. - **Slovjanske sravnenja / comparanda:** ru: польская нотация; uk: польська нотація; pl: notacja polska; cs: polská notace; bcs: poljska notacija; пољска нотација; bg: полска нотация. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[13106]; dictionary_id=2935); ISV-DICT-LIVE-20260825 (wordList[11842]; dictionary_id=36115); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** prefiksna notacija: The descriptive synonym is useful but loses the historical name used by the source. - **Neizvěstnost / uncertainty:** The complete historical compound is compositional rather than a direct row. ## OLISV-T0305 · logic.possibility - **English lemma / sense:** possibility — The modal status expressed by Diamond A, read as A holding in at least one accessible possible world. - **Medžuslovjansky:** `možlivosť`; lemma `možlivosť`; feminine noun. - **Upotrěbljenje / inflection:** Feminine možlivosť; genitive možlivosti. Use možlivo or može byti for predicative paraphrases. - **Kirilična forma:** `можливост` - **Argumentacija / rationale:** Možlivosť is the direct possibility head and pairs naturally with the established možlivy adjective. The source's abbreviation and possible-world wording fix the modal rather than ordinary-opportunity sense. - **Uvěrjenost / status:** 0.93 (high); `provisional`; revision `OLISV-T0305-r0001`. - **Slovjanske sravnenja / comparanda:** ru: возможность; uk: можливість; pl: możliwość; cs: možnost; bcs: mogućnost; bg: възможност. - **Dokazy / evidence:** OL-FOL-BEYOND-MODAL-LOGICS (lines 26-38); ISV-DICT-LIVE-20260825 (dictionary_id=2752; lemma=možlivosť; gloss=possibility, occasion); ISV-DICT-LIVE-20260825 (dictionary_id=280; lemma=možlivy; gloss=possible); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** možnosť: The shorter form is common in some national traditions, but the pinned dictionary's možlivosť head and the edition's existing možlivy family make the longer surface explicit. - **Neizvěstnost / uncertainty:** The dictionary gloss includes occasion alongside possibility; the source context is required to select the modal sense. ## OLISV-T0306 · logic.possible-world - **English lemma / sense:** possible world — A world considered by the modal semantics as a point at which a formula may or may not hold. - **Medžuslovjansky:** `možlivy svět`; lemma `možlivy svět`; masculine adjective-noun phrase. - **Upotrěbljenje / inflection:** Masculine svět; plural možlive světy and genitive možlivogo světa. - **Kirilična forma:** `можливы свєт` - **Argumentacija / rationale:** Možlivy svět transparently combines the direct possible adjective with the direct world head and keeps the semantic locus visible to readers across scripts. It does not assert that possible worlds are concrete entities. - **Uvěrjenost / status:** 0.94 (high); `provisional`; revision `OLISV-T0306-r0001`. - **Slovjanske sravnenja / comparanda:** ru: возможный мир; uk: можливий світ; pl: możliwy świat; cs: možný svět; bcs: mogući svijet; bg: възможен свят. - **Dokazy / evidence:** OL-FOL-BEYOND-MODAL-LOGICS (lines 26-29, 35-38, and 43-48); ISV-DICT-LIVE-20260825 (dictionary_id=280; lemma=možlivy; gloss=possible); ISV-DICT-LIVE-20260825 (dictionary_id=3137; lemma=svět; gloss=world); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** alternativny svět: An alternative-world phrase can suggest a competing actual history rather than the source's modal semantic point and is less aligned with the direct možlivy evidence. - **Neizvěstnost / uncertainty:** Possible-world ontology is philosophically contested; the term names the source's semantic device and not a metaphysical commitment. ## OLISV-T0083 · logic.predicate - **English lemma / sense:** predicate — A nonlogical relation symbol in a formal language, here exemplified by a binary symbol interpreted as a relation. - **Medžuslovjansky:** `predikat`; lemma `predikat`; masculine noun. - **Upotrěbljenje / inflection:** Genitive singular predikata; keep the logical sense separate from the grammatical predicate homonym. - **Kirilična forma:** `предикат` - **Argumentacija / rationale:** The frozen dictionary provides a dedicated logic-sense row and separates it from the grammatical homonym. - **Uvěrjenost / status:** 0.96 (high); `provisional`; revision `OLISV-T0083-r0001`. - **Slovjanske sravnenja / comparanda:** ru: предикат; uk: предикат; pl: predykat; cs: predikát; bcs: tvrdnja; predikat; bg: предикат. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[13292]; dictionary_id=36370); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** prisųdok: This belongs to grammatical predication rather than the logical relation-symbol sense.; simbol odnošenja: Useful explanation but narrower than predicate once other arities enter. - **Neizvěstnost / uncertainty:** The Croatian dictionary cell diverges to tvrdnja. ## OLISV-T0229 · logic.predicate-quantification - **English lemma / sense:** quantification over predicates — Quantification whose bound variables range over predicates, used here to characterize the boundary between first-order and second- or higher-order systems. - **Medžuslovjansky:** `kvantifikacija nad predikatami`; lemma `kvantifikacija nad predikatami`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive kvantifikacije nad predikatami; nad governs instrumental plural here and keeps the quantified-over relation explicit. - **Kirilična forma:** `квантификација над предикатами` - **Argumentacija / rationale:** The operation is not a duplicate of the quantifier or predicate heads: its added content is the range of the bound variables. Nad plus instrumental plural makes that relation explicit and aligns especially well with the South-Slavic comparison forms. - **Uvěrjenost / status:** 0.84 (high); `provisional`; revision `OLISV-T0229-r0001`. - **Slovjanske sravnenja / comparanda:** ru: квантификация по предикатам; uk: квантифікація за предикатами; pl: kwantyfikacja po predykatach; cs: kvantifikace přes predikáty; bcs: kvantifikacija nad predikatima; квантификација над предикатима; bg: квантификация по предикати. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[13292]; dictionary_id=36370; lemma=predikat; gloss=predicate (logic)); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** kvantifikacija predikatov: A bare genitive can obscure whether predicates are quantified, quantified over, or merely associated with the operation. - **Neizvěstnost / uncertainty:** The frozen dictionary lacks a direct kvantifikacija lemma; the operation head is an editorial derivation from established kvantifikator.; The Croatian dictionary comparison row renders logical predicate as tvrdnja, unlike the other traditions. ## OLISV-T0127 · logic.predicate-symbol - **English lemma / sense:** predicate symbol — A nonlogical symbol of fixed arity interpreted as a relation in a structure. - **Medžuslovjansky:** `predikatny simbol`; lemma `predikatny simbol`; masculine noun phrase. - **Upotrěbljenje / inflection:** Genitive predikatnogo simbola; reserve predikat for the broader category or interpreted property where context allows. - **Kirilična forma:** `предикатны симбол` - **Argumentacija / rationale:** The compound preserves the syntactic-symbol type and reuses the directly attested logic predicate. - **Uvěrjenost / status:** 0.79 (medium); `provisional`; revision `OLISV-T0127-r0001`. - **Slovjanske sravnenja / comparanda:** ru: предикатный символ; uk: предикатний символ; pl: symbol predykatowy; cs: predikátový symbol; bcs: predikatni simbol; предикатски симбол; bg: предикатен символ. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[13292]; dictionary_id=36370); ISV-DICT-LIVE-20260825 (wordList[16812]; dictionary_id=12221); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** predikat: The bare noun risks conflating the object-language symbol with its interpreted relation. - **Neizvěstnost / uncertainty:** The complete compound is compositional rather than directly attested. ## OLISV-T0240 · logic.predicative - **English lemma / sense:** predicative — A comprehension restriction that forbids second-order quantifiers in the defining formula. - **Medžuslovjansky:** `predikativny`; lemma `predikativny`; hard adjective. - **Upotrěbljenje / inflection:** Use predikativna forma tvorjenja and predikativno opreděljenje; the adjective agrees with the noun. - **Kirilična forma:** `предикативны` - **Argumentacija / rationale:** Predikativny is the established international counterpart to the source's restriction and transparently relates to the existing predikat canon entry. The target preserves the weaker-than-full qualification. - **Uvěrjenost / status:** 0.79 (high); `provisional`; revision `OLISV-T0240-r0002`. - **Slovjanske sravnenja / comparanda:** ru: предикативный; uk: предикативний; pl: predykatywny; cs: predikativní; bcs: predikativan; предикативан; bg: предикативен. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (dictionary_id=36370; lemma=predikat; gloss=predicate (logic)); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** prvoredovy: Describes first-order syntax but not the philosophical/formal predicativity restriction.; neimpredikativny: A negative paraphrase is less idiomatic and hides the positive historical term. - **Neizvěstnost / uncertainty:** The adjective is an editorial specialist extension rather than a direct dictionary lemma.; The r0001 record remains preserved as adverse provenance for the target/source locator mismatch. ## OLISV-T0164 · logic.premise - **English lemma / sense:** premise — A proposition or formula used as an input to an inference; here the extra existence claim required for existential generalization in free logic. - **Medžuslovjansky:** `premisa`; lemma `premisa`; feminine noun. - **Upotrěbljenje / inflection:** Genitive singular premisy; plural premisy. Reserve prědpoklad for an assumption when the inferential premise role is not intended. - **Kirilična forma:** `премиса` - **Argumentacija / rationale:** Premisa supplies a compact specialist head that is directly conventional in Czech and BCS and internationally transparent elsewhere. It avoids the false friend posylka, whose frozen dictionary sense is only a parcel, while distinguishing an inference input from a generic assumption. - **Uvěrjenost / status:** 0.66 (medium); `provisional`; revision `OLISV-T0164-r0001`. - **Slovjanske sravnenja / comparanda:** ru: посылка; uk: засновок; pl: przesłanka; cs: premisa; bcs: premisa; премиса; bg: предпоставка. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-DICT-LIVE-20260825 (wordList[12354], wordList[1270], wordList[16643]; dictionary_id=5751,5324,11247); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** posylka: The Russian logical cognate is a false friend in the frozen Interslavic dictionary, where posylka means only a package or parcel.; prědpoklad: Directly attested for assumption, but broader than the inferential input role and less compactly conventional in the source construction. - **Neizvěstnost / uncertainty:** Premisa is an edition-level specialist adoption rather than a frozen-dictionary headword.; Russian, Ukrainian, Polish, and Bulgarian traditions prefer different native heads. ## OLISV-T0106 · logic.primitive-symbol - **English lemma / sense:** primitive symbol — A symbol taken as basic rather than introduced by an explicit abbreviation. - **Medžuslovjansky:** `primitivny simbol`; lemma `primitivny simbol`; masculine noun phrase. - **Upotrěbljenje / inflection:** Genitive primitivnogo simbola; contrast with definovany simbol. - **Kirilična forma:** `примитивны симбол` - **Argumentacija / rationale:** Both components are directly attested and internationally convergent. - **Uvěrjenost / status:** 0.88 (high); `provisional`; revision `OLISV-T0106-r0001`. - **Slovjanske sravnenja / comparanda:** ru: примитивный символ; uk: примітивний символ; pl: symbol pierwotny; cs: primitivní symbol; bcs: primitivni simbol; примитивни симбол; bg: примитивен символ. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[13417]; dictionary_id=35198); ISV-DICT-LIVE-20260825 (wordList[16812]; dictionary_id=12221); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** osnovny simbol: Osnovny is transparent but does not preserve the established primitive/defined technical opposition. - **Neizvěstnost / uncertainty:** The complete compound is compositionally rather than directly attested. ## OLISV-T0320 · logic.probabilistic - **English lemma / sense:** probabilistic logic — A logic designed in the source to model reasoning involving uncertainty through probabilistic structure. - **Medžuslovjansky:** `věrojętnostna logika`; lemma `věrojętnostna logika`; feminine derived-adjective noun phrase. - **Upotrěbljenje / inflection:** Feminine logika; genitive věrojętnostnoj logiky and plural věrojętnostne logiky. - **Kirilična forma:** `вєројетностна логика` - **Argumentacija / rationale:** Věrojętnostna logika derives a transparent adjective from the frozen probability head and pairs it with the stable logic noun. The source's uncertainty sentence determines the intended probabilistic field rather than generic likelihood talk. - **Uvěrjenost / status:** 0.9 (high); `provisional`; revision `OLISV-T0320-r0001`. - **Slovjanske sravnenja / comparanda:** ru: вероятностная логика; uk: ймовірнісна логіка; pl: logika probabilistyczna; cs: pravděpodobnostní logika; bcs: vjerojatnosna logika; вероватносна логика; bg: вероятностна логика. - **Dokazy / evidence:** OL-FOL-BEYOND-OTHER-LOGICS (lines 24-25); ISV-DICT-LIVE-20260825 (dictionary_id=13576; lemma=věrojętnosť; gloss=probability, likelihood); ISV-DICT-LIVE-20260825 (dictionary_id=8933; lemma=logika; gloss=logic); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** probabilistična logika: The international form is searchable but less immediately transparent than the strongly attested věrojętnost family across East and South Slavic. - **Neizvěstnost / uncertainty:** The adjective is productively derived from the listed noun rather than separately attested as a frozen dictionary head. ## OLISV-T0144 · logic.proper-prefix - **English lemma / sense:** proper prefix — A prefix strictly shorter than the complete string, equivalently one whose concatenation with a non-empty suffix yields the string. - **Medžuslovjansky:** `strogy prefiks`; lemma `strogy prefiks`; masculine noun phrase. - **Upotrěbljenje / inflection:** Genitive strogogo prefiksa; strogy marks strict inclusion and must not be read as severity. - **Kirilična forma:** `строгы префикс` - **Argumentacija / rationale:** The canonical mathematical strictness adjective blocks the competing everyday own sense of vlastny while the source definition supplies the exact shorter-prefix condition. - **Uvěrjenost / status:** 0.82 (medium); `provisional`; revision `OLISV-T0144-r0001`. - **Slovjanske sravnenja / comparanda:** ru: собственный префикс; uk: власний префікс; pl: prefiks właściwy; cs: vlastní prefix; bcs: pravi prefiks; прави префикс; bg: същински префикс. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[16395]; dictionary_id=12676); ISV-DICT-LIVE-20260825 (wordList[13310]; dictionary_id=805); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** vlastny prefiks: Vlastny is conventional for proper in several traditions but also directly means one's own, creating avoidable ambiguity for a receptive interlanguage readership. - **Neizvěstnost / uncertainty:** National specialist traditions often use cognates of vlastny/proper; the edition selects the less ambiguous strictness paraphrase. ## OLISV-T0149 · logic.proper-subformula - **English lemma / sense:** proper subformula — A subformula of a formula that is not identical to the formula itself; recursively, it includes all proper subformulas of the immediate components. - **Medžuslovjansky:** `stroga podformula`; lemma `stroga podformula`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive stroge podformuly; the strictness adjective agrees with feminine podformula and reuses the canonical mathematical sense selected for proper prefix. - **Kirilična forma:** `строга подформула` - **Argumentacija / rationale:** Stroga reuses the canon's strict-inclusion adjective from proper prefix, making the exclusion of the whole formula explicit and avoiding the everyday own-sense ambiguity of vlastna. The source's recursive clauses supply the exact formal boundary. - **Uvěrjenost / status:** 0.82 (medium); `provisional`; revision `OLISV-T0149-r0001`. - **Slovjanske sravnenja / comparanda:** ru: собственная подформула; uk: власна підформула; pl: właściwa podformuła; cs: vlastní podformule; bcs: prava/vlastita podformula; права/властита подформула; bg: собствена подформула. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-GRAMMAR-ADJ (lines 14-18); ISV-DICT-LIVE-20260825 (wordList[16395]; dictionary_id=12676); ISV-DICT-LIVE-20260825 (wordList[13310]; dictionary_id=805); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** vlastna podformula: Vlastna is familiar as a translation of proper in several national traditions, but it can also mean one's own; stroga keeps the strict-subset relation transparent and consistent with the existing canon. - **Neizvěstnost / uncertainty:** The complete compound is an edition-level specialist selection rather than a direct dictionary headword.; Some national textbooks prefer vlastna/sobstvena-type adjectives; that variation remains visible in the comparanda and rejection record.; No official or native certification is claimed for the complete specialist compound. ## OLISV-T0140 · logic.property - **English lemma / sense:** property — A condition or characteristic that may be borne by mathematical objects, including numbers, as well as by syntactic or semantic classes. - **Medžuslovjansky:** `svojstvo`; lemma `svojstvo`; neuter noun. - **Upotrěbljenje / inflection:** Genitive svojstva; in induction clauses say svojstvo važi for an expression. - **Kirilična forma:** `својство` - **Argumentacija / rationale:** The direct lemma is pan-Slavically transparent and its dictionary columns already span property and characteristic readings. The dedicated OLP-0179 unit now broadens the current sense while the earlier revision remains preserved as scope provenance. - **Uvěrjenost / status:** 0.94 (high); `provisional`; revision `OLISV-T0140-r0002`. - **Slovjanske sravnenja / comparanda:** ru: свойство, характеристика; uk: властивість, риса, характеристика; pl: cecha; cs: vlastnost, chrakteristika, rys; bcs: svojstvo, karakteristika; својство, особина; bg: свойства. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 20-21 and 63-72); ISV-DICT-LIVE-20260825 (wordList[3203]; dictionary_id=22019); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** osobina: The alternative is common for traits but less stable in formal mathematical predication across the comparison languages. - **Neizvěstnost / uncertainty:** Polish and Czech mathematical usage often prefers własność/vlastnost rather than the dictionary's more general cecha comparandum.; Earlier narrower sense wording remains preserved in the superseded revision. ## OLISV-T0279 · logic.proposition - **English lemma / sense:** proposition — A truth-apt claim represented by a propositional variable in the Kripke explanation. - **Medžuslovjansky:** `tvrdženje`; lemma `tvrdženje`; neuter verbal noun. - **Upotrěbljenje / inflection:** Neuter tvrdženje; plural tvrdženja, genitive tvrdženja. - **Kirilična forma:** `тврджење` - **Argumentacija / rationale:** Tvrdženje conveys a truth-apt statement across the Slavic comparison and avoids presenting the dictionary's ordinary proposal sense as the logical noun. Propozicijsky remains the established adjective for the system and variables. - **Uvěrjenost / status:** 0.83 (high); `provisional`; revision `OLISV-T0279-r0001`. - **Slovjanske sravnenja / comparanda:** ru: высказывание; uk: висловлювання; pl: zdanie; cs: výrok; bcs: tvrdnja; исказ; bg: твърдение. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 200-210); ISV-DICT-LIVE-20260825 (dictionary_id=1087; lemma=tvŕđeńje; gloss=statement, claim, assertion); ISV-DICT-LIVE-20260825 (dictionary_id=5124; lemma=propozicija; gloss=proposal); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** propozicija: The pinned direct gloss is proposal, creating an avoidable false friend when the source requires a claim known to be true. - **Neizvěstnost / uncertainty:** Some specialist traditions use international proposition forms; the edition deliberately separates the noun from the established propozicijsky adjective. ## OLISV-T0119 · logic.propositional-constant - **English lemma / sense:** propositional constant — A zero-argument logical symbol with a fixed truth value. - **Medžuslovjansky:** `propozicijska konstanta`; lemma `propozicijska konstanta`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive propozicijskoj konstanty; here the head denotes the logical symbol, not an arbitrary stable quantity. - **Kirilična forma:** `пропозицијска константа` - **Argumentacija / rationale:** The international compound matches established edition usage and all national specialist traditions. - **Uvěrjenost / status:** 0.8 (medium); `provisional`; revision `OLISV-T0119-r0001`. - **Slovjanske sravnenja / comparanda:** ru: пропозициональная константа; uk: пропозиційна константа; pl: stała zdaniowa; cs: výroková konstanta; bcs: propozicijska konstanta; пропозициона константа; bg: пропозиционална константа. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** istinnostna konstanta: The descriptive alternative is transparent but less established than the source's propositional terminology. - **Neizvěstnost / uncertainty:** No exact frozen dictionary row attests the complete compound. ## OLISV-T0280 · logic.propositional-language - **English lemma / sense:** propositional language — A formal language of propositional variables and connectives interpreted by valuations or Kripke structures. - **Medžuslovjansky:** `propozicijsky jezyk`; lemma `propozicijsky jezyk`; masculine adjective-noun phrase. - **Upotrěbljenje / inflection:** Masculine jezyk; genitive propozicijskogo jezyka. The dictionary język spelling is normalized to the edition's jezyk surface. - **Kirilična forma:** `пропозицијскы језык` - **Argumentacija / rationale:** The phrase extends the edition's established propozicijsky system adjective to the direct language head; the exact source context prevents the ordinary proposal reading. - **Uvěrjenost / status:** 0.84 (high); `provisional`; revision `OLISV-T0280-r0001`. - **Slovjanske sravnenja / comparanda:** ru: пропозициональный язык; uk: пропозиційна мова; pl: język zdaniowy; cs: výrokový jazyk; bcs: propozicijski jezik; исказни језик; bg: пропозиционален език. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 180-184 and 200-210); ISV-DICT-LIVE-20260825 (dictionary_id=541; lemma=język; gloss=language); ISV-DICT-LIVE-20260825 (dictionary_id=5124; lemma=propozicija; gloss=proposal); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** jezyk tvrdženj: Readable but inconsistent with the established propozicijska logika and propozicijska prěměnna families. - **Neizvěstnost / uncertainty:** The full compound is source-defined rather than directly listed in the dictionary, and national languages vary between proposition and statement roots. ## OLISV-T0278 · logic.propositional-logic - **English lemma / sense:** propositional logic — A logical system whose formulas are built from propositional variables and connectives. - **Medžuslovjansky:** `propozicijska logika`; lemma `propozicijska logika`; feminine adjective-noun phrase. - **Upotrěbljenje / inflection:** Feminine logika; genitive propozicijskoj logiky. - **Kirilična forma:** `пропозицијска логика` - **Argumentacija / rationale:** Propozicijska logika is already the edition's stable, internationally searchable system label. The ordinary proposal gloss is retained as adverse evidence, so the source—not that gloss—fixes the logical sense. - **Uvěrjenost / status:** 0.84 (high); `provisional`; revision `OLISV-T0278-r0001`. - **Slovjanske sravnenja / comparanda:** ru: логика высказываний; uk: логіка висловлювань; pl: logika zdań; cs: výroková logika; bcs: propozicijska logika; исказна логика; bg: логика на съжденията. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 128-149); ISV-DICT-LIVE-20260825 (dictionary_id=8933; lemma=logika; gloss=logic); ISV-DICT-LIVE-20260825 (dictionary_id=5124; lemma=propozicija; gloss=proposal); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** logika tvrdženj: Transparent, but it would diverge from the established chapter label and much South-Slavic specialist usage. - **Neizvěstnost / uncertainty:** Propozicija alone means proposal in the pinned dictionary; only the qualified specialist adjective is preferred here. ## OLISV-T0168 · logic.propositional-valuation - **English lemma / sense:** propositional valuation — A function that assigns a truth value to every propositional variable and thereby determines the truth values of formulas. - **Medžuslovjansky:** `ocěnka`; lemma `ocěnka`; feminine noun. - **Upotrěbljenje / inflection:** Genitive singular and nominative plural ocěnky. On first use, the technical sense may be expanded as ocěnka propozicijskih prěměnnyh. Keep funkcija vrednovanja for the recursively extended evaluation function, not for the initial valuation itself. - **Kirilična forma:** `оцєнка` - **Argumentacija / rationale:** Ocěnka is selected because the pinned published dictionary directly lists that Interslavic lemma with valuation in its English sense inventory and exposes an unusually broad East, West, and South Slavic cognate pattern. The Open Logic definition restricts the polysemous general noun to the function assigning truth values to propositional variables. The edition keeps funkcija vrednovanja for the separate recursive extension from all formulas to truth values, preserving the source's distinction between valuation and evaluation. - **Uvěrjenost / status:** 0.84 (medium); `provisional`; revision `OLISV-T0168-r0001`. - **Slovjanske sravnenja / comparanda:** ru: оценка; uk: оцінка; pl: ocena; cs: ohodnocení; bcs: ocjena; оцена; bg: оценка. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[10768]; dictionary_id=29019; lemma=ocěnka; English gloss includes valuation); ISV-GRAMMAR-ADJ (declension framework used by the edition; noun form checked against the published dictionary row); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** vrednovanje: Recognizable in several South and West Slavic traditions, but in the current edition it already denotes the recursively extended evaluation function; using it for both levels would erase a source distinction.; prisvajanje istinnyh cěnnostij: Transparent but long, and prisvajanje is already the edition's canonical head for first-order variable assignment; the expansion remains available as an explanatory gloss rather than the recurring token.; valuacija: Internationally recognizable but lacks the selected candidate's direct pinned Interslavic dictionary attestation and its cross-family cognate support in this evidence set. - **Neizvěstnost / uncertainty:** The direct dictionary row is polysemous and does not independently certify specialist logical usage.; Polish, Czech, and parts of South Slavic specialist traditions may prefer derivatives of value or evaluation rather than the selected ocěn- family. ## OLISV-T0311 · logic.provability - **English lemma / sense:** provability logic — A modal application in which Box A is read as A being provable and Diamond A as A being consistent. - **Medžuslovjansky:** `logika dokazlivosti`; lemma `logika dokazlivosti`; feminine noun phrase. - **Upotrěbljenje / inflection:** Feminine logika; genitive logiky dokazlivosti. - **Kirilična forma:** `логика доказливости` - **Argumentacija / rationale:** Logika dokazlivosti makes the source's provable reading compositional from the direct proof family. The source's consistency gloss remains a documented application-level simplification rather than a hidden lexical expansion. - **Uvěrjenost / status:** 0.84 (high); `provisional`; revision `OLISV-T0311-r0001`. - **Slovjanske sravnenja / comparanda:** ru: логика доказуемости; uk: логіка довідності; pl: logika dowodliwości; cs: logika dokazatelnosti; bcs: logika dokazivosti; bg: логика на доказуемостта. - **Dokazy / evidence:** OL-FOL-BEYOND-MODAL-LOGICS (lines 59-60); ISV-DICT-LIVE-20260825 (dictionary_id=7161; lemma=dokazati; gloss=prove); ISV-DICT-LIVE-20260825 (dictionary_id=2041; lemma=dokaz; gloss=proof, evidence); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** logika dokazov: A proof-objects phrase does not express the modal property of being provable and is less aligned with the national provability forms. - **Neizvěstnost / uncertainty:** The adjective dokazlivy is derived rather than directly listed in the frozen dictionary; the source fixes its modal application. ## OLISV-T0126 · logic.punctuation - **English lemma / sense:** punctuation — The commas and grouping marks included in the written vocabulary of the formal language. - **Medžuslovjansky:** `interpunkcija`; lemma `interpunkcija`; feminine noun. - **Upotrěbljenje / inflection:** Genitive interpunkcije; use znak interpunkcije for one punctuation mark. - **Kirilična forma:** `интерпункција` - **Argumentacija / rationale:** Direct international lemma has strong national convergence. - **Uvěrjenost / status:** 0.9 (high); `provisional`; revision `OLISV-T0126-r0001`. - **Slovjanske sravnenja / comparanda:** ru: пунктуация; uk: пунктуація; pl: interpunkcja; cs: interpunkce; bcs: interpunkcija, razgodak; интерпункција, правописни знаци; bg: пунктуация. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[13662]; dictionary_id=23620); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** punktuacija: A competing internationalism appears in some drafts but is less aligned with the frozen direct lemma. - **Neizvěstnost / uncertainty:** Serbian and Bulgarian comparanda also use analytic phrases for punctuation marks. ## OLISV-T0292 · logic.pure-logic - **English lemma / sense:** pure logic — The logical calculus considered without adding mathematical nonlogical axioms. - **Medžuslovjansky:** `čista logika`; lemma `čista logika`; feminine adjective-noun phrase. - **Upotrěbljenje / inflection:** Feminine logika; genitive čistoj logiky. - **Kirilična forma:** `чиста логика` - **Argumentacija / rationale:** Čista logika is a direct transparent compound whose source context fixes pure as axiom-free logical scope rather than cleanliness. - **Uvěrjenost / status:** 0.97 (high); `provisional`; revision `OLISV-T0292-r0001`. - **Slovjanske sravnenja / comparanda:** ru: чистая логика; uk: чиста логіка; pl: czysta logika; cs: čistá logika; bcs: čista logika; чиста логика; bg: чиста логика. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 166-170); ISV-DICT-LIVE-20260825 (dictionary_id=582; lemma=čisty; gloss=clean, pure, chaste); ISV-DICT-LIVE-20260825 (dictionary_id=8933; lemma=logika; gloss=logic); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** sama logika: Can mean logic alone rhetorically, but does not provide a stable specialist label. - **Neizvěstnost / uncertainty:** The adjective is broadly polysemous; the adjacent contrast supplies the precise technical sense. ## OLISV-T0221 · logic.purely-logical-sentence - **English lemma / sense:** purely logical sentence — A sentence using logical or equality vocabulary but no nonlogical symbols; not a synonym for every well-formed logical sentence. - **Medžuslovjansky:** `čisto logično izrečenje`; lemma `čisto logično izrečenje`; neuter adverb-adjective-noun phrase. - **Upotrěbljenje / inflection:** Neuter phrase; genitive čisto logičnogo izrečenja. Use izrečenje bez nelogičnyh simbolov as an explicit definitional paraphrase. - **Kirilična forma:** `чисто логично изречење` - **Argumentacija / rationale:** The adverb-adjective construction closely converges across the six comparison traditions and preserves the source contrast with sentences containing nonlogical predicates. Existing canon entries supply izrečenje and the opposed nelogičny simbol family. - **Uvěrjenost / status:** 0.86 (high); `provisional`; revision `OLISV-T0221-r0001`. - **Slovjanske sravnenja / comparanda:** ru: чисто логическое предложение; uk: суто логічне речення; pl: zdanie czysto logiczne; cs: čistě logická věta; bcs: čisto logička rečenica; bg: чисто логическо изречение. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[3445]; dictionary_id=582; lemma=čisty; gloss=clean, pure, chaste); ISV-DICT-LIVE-20260825 (wordList[10432]; dictionary_id=363; lemma=logičny; gloss=logical); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** samo logično izrečenje: Samo can mean merely or only and may be read as limiting the count or discourse status of the sentence rather than excluding nonlogical vocabulary. - **Neizvěstnost / uncertainty:** Čisty is directly frozen only in a generic purity sense; the specialist meaning is fixed by the source's explicit absence-of-nonlogical-symbols boundary. ## OLISV-T0100 · logic.quantifier - **English lemma / sense:** quantifier — A logical operator binding a variable over a domain of discourse. - **Medžuslovjansky:** `kvantifikator`; lemma `kvantifikator`; masculine noun. - **Upotrěbljenje / inflection:** Genitive kvantifikatora; qualify as universalny or eksistencialny when the force matters. - **Kirilična forma:** `квантификатор` - **Argumentacija / rationale:** The international form is stable and immediately recognizable across the Slavic specialist traditions. - **Uvěrjenost / status:** 0.78 (medium); `provisional`; revision `OLISV-T0100-r0001`. - **Slovjanske sravnenja / comparanda:** ru: квантор; uk: квантор; pl: kwantyfikator; cs: kvantifikátor; bcs: kvantifikator; квантификатор; bg: квантор. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** količnik: A native-looking calque is not established for the binding operator and risks an arithmetic reading. - **Neizvěstnost / uncertainty:** The preferred form is source-bounded and editorial rather than a direct dictionary lemma. ## OLISV-T0235 · logic.quantifier-relativization - **English lemma / sense:** quantifier relativization — Replacing a sorted quantifier by an ordinary quantifier guarded by a predicate that selects the intended sort domain. - **Medžuslovjansky:** `relativizacija kvantifikatorov`; lemma `relativizacija kvantifikatorov`; feminine noun phrase with genitive plural. - **Upotrěbljenje / inflection:** Genitive relativizacije kvantifikatorov; use relativizovati kvantifikator k predikatu when a verbal clause is needed. - **Kirilična forma:** `релативизација квантификаторов` - **Argumentacija / rationale:** The international operation name precisely identifies predicate-guard restriction and composes with established kvantifikator. - **Uvěrjenost / status:** 0.8 (high); `provisional`; revision `OLISV-T0235-r0001`. - **Slovjanske sravnenja / comparanda:** ru: релятивизация кванторов; uk: релятивізація кванторів; pl: relatywizacja kwantyfikatorów; cs: relativizace kvantifikátorů; bcs: relativizacija kvantifikatora; релативизација квантификатора; bg: релативизация на кванторите. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[14176]; dictionary_id=35263; lemma=odnositeljny; gloss=relative); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** ograničenje kvantifikatorov: Useful explanatory wording, but broader than guard-predicate relativization. - **Neizvěstnost / uncertainty:** The dictionary pins the relative family rather than a direct relativizacija headword. ## OLISV-T0155 · logic.quantifier-scope - **English lemma / sense:** scope of a quantifier occurrence — The corresponding occurrence of the immediate subformula governed by a quantifier occurrence inside a containing formula. - **Medžuslovjansky:** `obseg kvantifikatora`; lemma `obseg kvantifikatora`; masculine noun phrase. - **Upotrěbljenje / inflection:** Genitive obsega kvantifikatora. The etymological TeX reader displays obsęg; oblast dějstvovanja remains an explanatory synonym, not a second canon head. - **Kirilična forma:** `обсег квантификатора` - **Argumentacija / rationale:** Obseg is the standard-Latin machine form of the directly listed scope lemma obsęg and gives a concise head recognizable especially in West and South Slavic. The exact source definition prevents the broad dictionary senses coverage and perimeter from leaking into the logical term. - **Uvěrjenost / status:** 0.84 (medium); `provisional`; revision `OLISV-T0155-r0001`. - **Slovjanske sravnenja / comparanda:** ru: область действия квантора; uk: область дії квантора; pl: zakres kwantyfikatora; cs: obor platnosti kvantifikátoru; bcs: opseg kvantifikatora; опсег квантификатора; bg: обхват на квантора. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-DICT-LIVE-20260825 (wordList[14910]; dictionary_id=28929); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** oblast dějstvovanja kvantifikatora: This established explanatory phrase is transparent and retained at first-use or pedagogical loci, but it is longer and less suitable as the repeated compact head than the directly listed scope lemma.; sfera kvantifikatora: The international noun is recognizable but remains a broad spatial metaphor and lacks the direct scope gloss carried by obsęg. - **Neizvěstnost / uncertainty:** The direct lemma is broad outside logic; the source locator supplies the formal governance sense.; Standard-Latin obseg and etymological-display obsęg are two surfaces of the same term.; No native or official certification is claimed for the complete specialist compound. ## OLISV-T0255 · logic.relation-variable - **English lemma / sense:** relation variable — A variable ranging over relations of a fixed arity in a second-order language. - **Medžuslovjansky:** `prěměnna odnošenja`; lemma `prěměnna odnošenja`; feminine noun phrase. - **Upotrěbljenje / inflection:** Plural prěměnne odnošenja; genitive prěměnnoj odnošenja. The arity is stated with a městnost adjective. - **Kirilična forma:** `прємєнна одношења` - **Argumentacija / rationale:** The phrase combines the two direct logical heads already established in the canon and exactly states the source's fixed-arity range. It makes the second-order variable status explicit without introducing a separate relation-domain head. - **Uvěrjenost / status:** 0.93 (high); `provisional`; revision `OLISV-T0255-r0002`. - **Slovjanske sravnenja / comparanda:** ru: переменная отношения; uk: змінна відношення; pl: zmienna relacji; cs: relační proměnná; bcs: prоменljiva relacije; променљива релације; bg: променлива на отношение. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (dictionary_id=35526; lemma=prěměnna; gloss=variable); ISV-DICT-LIVE-20260825 (dictionary_id=1992; lemma=odnošeńje; gloss=relation, relationship, ratio); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** prěměnna predikata: Too narrow: the source ranges over arbitrary relations, not only predicates.; odnošeńny term: Loses the variable category and conflicts with the source's term/inference distinction. - **Neizvěstnost / uncertainty:** National traditions alternate relation variable and predicate variable; the source's arity condition motivates the broader term.; The r0001 record remains preserved as adverse provenance for the target/source locator mismatch. ## OLISV-T0069 · logic.satisfaction - **English lemma / sense:** satisfaction; satisfy — The semantic relation in which a structure, under a variable assignment where relevant, makes a formula true. - **Medžuslovjansky:** `zadovoljenje`; lemma `zadovoljenje`; neuter noun. - **Upotrěbljenje / inflection:** Use zadovolnjati for the verb: struktura zadovolnjaje formulu; the participle is zadovolnjeny. - **Kirilična forma:** `задовољење` - **Argumentacija / rationale:** Zadovoljenje keeps the already established edition family zadovolnjati–zadovoljivy coherent and is immediately recognizable in East and South Slavic. The Open Logic definition narrows the general satisfy family to the structure-assignment-formula relation, while the strong West Slavic fulfil-family alternative remains explicit. - **Uvěrjenost / status:** 0.68 (medium); `provisional`; revision `OLISV-T0069-r0001`. - **Slovjanske sravnenja / comparanda:** ru: удовлетворение; удовлетворять; uk: задоволення; задовольняти; pl: spełnianie; spełniać; cs: splňování; splňovat; bcs: zadovoljavanje; zadovoljavati; bg: изпълнение; изпълнявам. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[14811]; dictionary_id=444; lemma=zadovaljati; gloss=satisfy, please); ISV-DICT-LIVE-20260825 (wordList[14808]; dictionary_id=3318; lemma=zadovoljstvo; gloss=satisfaction); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** izpȯlnjenje: Strong in Polish, Czech, and Bulgarian comparanda, but changing roots would split satisfaction from the edition's established satisfiability family.; zadovoljstvo: Directly listed but primarily denotes personal contentment rather than the formal semantic relation. - **Neizvěstnost / uncertainty:** No registered dictionary row directly attests zadovoljenje in the formal model-theoretic sense.; West Slavic and Bulgarian specialist traditions favor an izpȯln- or fulfil-family root. ## OLISV-T0070 · logic.satisfiability - **English lemma / sense:** satisfiability — The property of a formula or set of sentences for which some structure, with a suitable assignment where relevant, satisfies it or all members simultaneously. - **Medžuslovjansky:** `zadovoljivost`; lemma `zadovoljivost`; feminine abstract noun. - **Upotrěbljenje / inflection:** Use zadovoljivy for satisfiable and nezadovoljivy for unsatisfiable; do not collapse the property into zadovoljenje. - **Kirilična forma:** `задовољивост` - **Argumentacija / rationale:** Zadovoljivost preserves the edition's established satisfaction-family distinction: zadovoljenje names the relation and zadovoljivost the existential property. The compact form is especially transparent to South Slavic readers, while the recorded comparanda expose the competing fulfil-family tradition. - **Uvěrjenost / status:** 0.66 (medium); `provisional`; revision `OLISV-T0070-r0001`. - **Slovjanske sravnenja / comparanda:** ru: выполнимость; удовлетворимость; uk: виконуваність; задовільність; pl: spełnialność; cs: splnitelnost; bcs: zadovoljivost; bg: изпълнимост; удовлетворимост. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[14809]; dictionary_id=37250; lemma=zadovoliteljny; gloss=satisfactory); ISV-DICT-LIVE-20260825 (wordList[3814-3815]; dictionary_id=597,2501; lemma=izpȯlniti, izpȯlnjati); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** izpȯlnimost: Strongly motivated by Polish, Czech, Bulgarian, and Russian comparanda, but it would break the accepted edition's satisfaction-family continuity.; zadovoliteljnost: The directly listed adjective means satisfactory, not logically satisfiable. - **Neizvěstnost / uncertainty:** The abstract noun is an edition-level derivation rather than a directly listed dictionary lemma.; Cross-Slavic specialist usage divides between zadovolj- and fulfil-family formations. ## OLISV-T0224 · logic.second-order - **English lemma / sense:** second-order logic — The second-order subtype named here; in Quine's attributed characterization it belongs to systems involving quantification over predicates. - **Medžuslovjansky:** `logika drugogo reda`; lemma `logika drugogo reda`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive logiky drugogo reda. Treat as a subtype of logika vyššego reda, not as a synonym for every higher-order framework. - **Kirilična forma:** `логика другого реда` - **Argumentacija / rationale:** The dedicated searchable subtype is compositionally parallel to T0090 but carries a distinct quantificational boundary. Drugy balances West and South Slavic convergence and the frozen dictionary against the recognizable East-Slavic vtor- alternative. - **Uvěrjenost / status:** 0.89 (high); `provisional`; revision `OLISV-T0224-r0001`. - **Slovjanske sravnenja / comparanda:** ru: логика второго порядка; uk: логіка другого порядку; pl: logika drugiego rzędu; cs: logika druhého řádu; bcs: logika drugog reda; логика другог реда; bg: логика от втори ред. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[10431]; dictionary_id=8933; lemma=logika; gloss=logic); ISV-DICT-LIVE-20260825 (wordList[14985]; dictionary_id=784; lemma=drugy; gloss=second); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** logika vtorogo reda: The East-Slavic and Bulgarian alternative is recognizable, but the frozen drugy component and West/South convergence make drugogo the broader project compromise. - **Neizvěstnost / uncertainty:** Second-order logic has multiple semantic formulations; this entry records the source's predicate-quantification contrast rather than choosing one semantics. ## OLISV-T0177 · logic.semantic-consequence-closure - **English lemma / sense:** closure under semantic consequence — For a sentence set Gamma, the set of every sentence semantically entailed by Gamma; Gamma is closed when it already contains every such consequence. - **Medžuslovjansky:** `zatvorjenje po semantičnom slědovanju`; lemma `zatvorjenje po semantičnom slědovanju`; neuter noun phrase. - **Upotrěbljenje / inflection:** Zatvorjenje is neuter; use genitive zatvorjenja. In nearby prose, zatvorjenje is permitted after the semantic consequence relation is explicit. - **Kirilična forma:** `затворјење по семантичном слєдовању` - **Argumentacija / rationale:** The longer head makes the closure operator's governing relation explicit and reuses the edition's established zatvorjenje head from OLISV-T0045. The source definition fixes this as semantic, not proof-theoretic, closure; ordinary prose may shorten the term once that relation is visible. - **Uvěrjenost / status:** 0.76 (medium); `provisional`; revision `OLISV-T0177-r0001`. - **Slovjanske sravnenja / comparanda:** ru: замыкание по семантическому следованию; uk: замикання за семантичним слідуванням; pl: domknięcie ze względu na wynikanie semantyczne; cs: uzávěr vzhledem k sémantickému vyplývání; bcs: zatvorenje po semantičkom slijeđenju; bg: затваряне спрямо семантичното следване. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[3510]; dictionary_id=31523; lemma=zamknųty; gloss=closed); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** zamknjenje po semantičnom slědovanju: The zamk- family is strong in East and West Slavic, but the established edition closure head zatvorjenje is more transparent to South Slavic readers and avoids a needless canon split. - **Neizvěstnost / uncertainty:** No frozen dictionary row directly attests the full specialist phrase.; National traditions divide between zamyk-/domk-/uzávěr and zatvor- closure families. ## OLISV-T0072 · logic.semantic-entailment - **English lemma / sense:** semantic entailment — The relation Γ entails A when every structure satisfying every sentence in Γ also satisfies A. - **Medžuslovjansky:** `slědovanje`; lemma `slědovanje`; neuter abstract noun. - **Upotrěbljenje / inflection:** Use semantično slědovanje where contrast with syntactic derivability is active; otherwise the short form slědovanje is sufficient. - **Kirilična forma:** `слєдовање` - **Argumentacija / rationale:** Slědovanje keeps the highly recognizable follow/consequence root, matches established edition usage, and names a relation rather than only its result. The optional semantično modifier prevents confusion with syntactic derivability where both relations occur together. - **Uvěrjenost / status:** 0.77 (medium); `provisional`; revision `OLISV-T0072-r0001`. - **Slovjanske sravnenja / comparanda:** ru: логическое следование; uk: логічне слідування; логічне випливання; pl: wynikanie logiczne; cs: logické vyplývání; bcs: logičko slijeđenje; logička posljedica; bg: логическо следване. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[7134]; dictionary_id=1939; lemma=slědovati; gloss=follow); ISV-DICT-LIVE-20260825 (wordList[4036-4037]; dictionary_id=2327,18328; lemma=poslědstvo, poslědica); ISV-DICT-LIVE-20260825 (wordList[6198-6199]; dictionary_id=35549,35550; lemma=povlěkati/povlěkti za sobojų; gloss=entail, involve); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** povlěčenje za sobojų: Dictionary-backed for general entail or involve but too periphrastic for a named binary metalogical relation.; semantična poslědica: Transparent but more readily names the consequent or result than the entailment relation itself. - **Neizvěstnost / uncertainty:** The dictionary directly attests the root but not the formal abstract noun.; Polish and Czech specialist traditions favor a distinct vypływ or consequence root. ## OLISV-T0092 · logic.semantics - **English lemma / sense:** semantics — Interpretive rules assigning values or satisfaction conditions to formal expressions. - **Medžuslovjansky:** `semantika`; lemma `semantika`; feminine noun. - **Upotrěbljenje / inflection:** Use genitive semantiky; retain the plural discipline sense only where context requires it. - **Kirilična forma:** `семантика` - **Argumentacija / rationale:** International lemma is identical or trivially adapted across all comparison languages. - **Uvěrjenost / status:** 0.96 (high); `provisional`; revision `OLISV-T0092-r0001`. - **Slovjanske sravnenja / comparanda:** ru: семантика; uk: семантика; pl: semantyka; cs: sémantika; bcs: semantika; семантика; bg: семантика. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[15062]; dictionary_id=35935); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** značenjeslovje: A native calque is not established across the national specialist traditions. - **Neizvěstnost / uncertainty:** Open Logic later gives the precise satisfaction clauses; this entry fixes only the discipline-level sense. ## OLISV-T0074 · logic.sentence - **English lemma / sense:** sentence — A formula containing no free occurrences of variables. - **Medžuslovjansky:** `izrečenje`; lemma `izrečenje`; neuter noun. - **Upotrěbljenje / inflection:** Use izrečenje as the short technical head and define it explicitly as formula bez svobodnyh pojavjenij prěmennyh; zamknuta formula remains a transparent explanatory synonym. - **Kirilična forma:** `изречење` - **Argumentacija / rationale:** Izrečenje preserves the accepted Open Logic head and remains directly recognizable in Bulgarian and South Slavic. OLP-0157 now supplies the exact occurrence-level definition. The earlier explanatory zamknjena formula is corrected to zamknuta formula from the directly listed zamknųty morphology and the byte-pinned accepted completeness text; this changes no preferred head or formal sense. - **Uvěrjenost / status:** 0.63 (medium); `provisional`; revision `OLISV-T0074-r0002`. - **Slovjanske sravnenja / comparanda:** ru: предложение; замкнутая формула; uk: речення; замкнена формула; pl: zdanie; formuła zamknięta; cs: věta; uzavřená formule; bcs: rečenica; zatvorena formula; bg: изречение; затворена формула. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[15099]; dictionary_id=3758; lemma=rěčeńje; gloss=sentence); ISV-DICT-LIVE-20260825 (wordList[3510-3511], wordList[7255]; dictionary_id=31523,2894,5181; lemma=zamknųty, zatvorjeny, formula); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** zamknuta formula: Precisely transparent and retained as a definitional synonym, but too long to replace every repeated token in continuous prose. The corrected participle follows direct dictionary morphology and accepted edition usage.; rěčenje: Directly listed and acceptable as a general sentence, but the accepted edition consistently uses the more distinctive prefixed form izrečenje. - **Neizvěstnost / uncertainty:** The preferred izrečenje is an edition continuity form rather than a directly listed dictionary lemma.; National specialist traditions divide between sentence-family heads and closed-formula compounds. ## OLISV-T0056 · logic.signed-formula - **English lemma / sense:** signed formula — A formula paired with a truth value, used as a node in a tableau proof. - **Medžuslovjansky:** `znakova formula`; lemma `znakova formula`; noun phrase. - **Upotrěbljenje / inflection:** Feminine noun phrase; znakova agrees with formula and refers to the attached truth sign, not to character encoding. - **Kirilična forma:** `знакова формула` - **Argumentacija / rationale:** Znakova formula is compositionally transparent and closely recognizable in East and South Slavic; the use note prevents confusion with typographic or encoding senses of sign. - **Uvěrjenost / status:** 0.72 (medium); `provisional`; revision `OLISV-T0056-r0001`. - **Slovjanske sravnenja / comparanda:** ru: знаковая формула; uk: знакова формула; pl: formuła ze znakiem; cs: znaménková formule; bcs: označena formula; bg: знакова формула. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** označena formula: Označena can mean merely marked or designated and does not as directly identify the attached truth-value sign. - **Neizvěstnost / uncertainty:** Polish and BCS comparanda favor analytic or participial forms; the edition compound remains provisional pending broader specialist-corpus evidence. ## OLISV-T0265 · logic.simple-type-theory - **English lemma / sense:** simple theory of types — The type-theoretic proof system associated with Church's 1930s formulation and the Omega truth-value extension. - **Medžuslovjansky:** `prosta teorija tipov`; lemma `prosta teorija tipov`; feminine noun phrase. - **Upotrěbljenje / inflection:** Feminine teorija; genitive proste teorije tipov. Use prosta as the normalized adjective agreeing with teorija. - **Kirilična forma:** `проста теорија типов` - **Argumentacija / rationale:** The source gives a named historical system, so the canon records a transparent compound built from the direct simple, theory, and type rows. The formal type-theoretic content remains explicit rather than being inferred from a generic logic label. - **Uvěrjenost / status:** 0.93 (high); `provisional`; revision `OLISV-T0265-r0002`. - **Slovjanske sravnenja / comparanda:** ru: простая теория типов; uk: проста теорія типів; pl: prosta teoria typów; cs: jednoduchá teorie typů; bcs: jednostavna teorija tipova; проста теорија типова; bg: проста теория на типовете. - **Dokazy / evidence:** OL-FOL-BEYOND-HIGHER-ORDER-LOGIC (lines 95-100); ISV-DICT-LIVE-20260825 (dictionary_id=3224; lemma=tip; gloss=type, kind); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3); ISV-DICT-LIVE-20260825 (dictionary_id=2334; lemma=prosty; gloss=simple, easy, plain); ISV-DICT-LIVE-20260825 (dictionary_id=4739; lemma=teorija; gloss=theory) - **Alternativy / alternatives:** teorija prostyh tipov: Changes simple as a property of the theory into a potentially restrictive subclass of types.; Churchova teorija: Drops the formal type-theoretic content and is not self-describing for new readers. - **Neizvěstnost / uncertainty:** The historical proper-name attribution is not encoded in the lexical head; readers should retain the source's Church attribution.; The r0001 record is preserved as adverse provenance for the evidence correction. ## OLISV-T0172 · logic.skolem-normal-form - **English lemma / sense:** Skolem normal form — The Skolemized form used here, replacing an existentially quantified dependent variable by a fresh function term while preserving satisfiability through a possibly expanded structure. - **Medžuslovjansky:** `Skolemova normalna forma`; lemma `Skolemova normalna forma`; feminine proper-name noun phrase. - **Upotrěbljenje / inflection:** Instrumental Skolemovoju normalnoju formoju and genitive Skolemovoj normalnoj formy. Preserve the source's equisatisfiability scope: the structures may differ. - **Kirilična forma:** `Сколемова нормална форма` - **Argumentacija / rationale:** The possessive Skolemova keeps the proper name visibly attached to the technical phrase, while normalna forma is maximally international and directly supported component by component. The definition records the source's expanded-structure and satisfiability boundary so the label does not imply same-structure equivalence. - **Uvěrjenost / status:** 0.85 (high); `provisional`; revision `OLISV-T0172-r0001`. - **Slovjanske sravnenja / comparanda:** ru: сколемовская нормальная форма; uk: сколемівська нормальна форма; pl: postać normalna Skolema; cs: Skolemův normální tvar; bcs: Skolemova normalna forma; Сколемова нормална форма; bg: сколемова нормална форма. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[7242]; dictionary_id=2001; lemma=forma; gloss=form); ISV-DICT-LIVE-20260825 (wordList[11797]; dictionary_id=5260; lemma=normaľny; gloss=normal); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** normalna forma Skolema: The genitive construction is grammatical and mirrors named theorems, but the possessive adjective more clearly modifies the entire form label and converges with Czech, BCS, Ukrainian, and Bulgarian patterns. - **Neizvěstnost / uncertainty:** The source uses the label for a single simple Skolemization pattern; broader textbooks may reserve Skolem normal form for a more completely normalized prenex formula.; Polish and Czech prefer different head nouns in specialist usage. ## OLISV-T0230 · logic.sort - **English lemma / sense:** sort — A category of objects in a many-sorted language, determining the domain a variable ranges over and the permitted argument positions. - **Medžuslovjansky:** `sort`; lemma `sort`; masculine inanimate noun. - **Upotrěbljenje / inflection:** Genitive sorta, plural sorty; use domen sorta and prěměnna někojego sorta. - **Kirilična forma:** `сорт` - **Argumentacija / rationale:** Sort is directly frozen and keeps the formal category distinct from the separate typing operation. - **Uvěrjenost / status:** 0.88 (high); `provisional`; revision `OLISV-T0230-r0001`. - **Slovjanske sravnenja / comparanda:** ru: сорт; тип; uk: сорт; тип; pl: sort; rodzaj; cs: sort; druh; bcs: sorta; vrsta; сорт; врста; bg: сорт; вид. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[9858]; dictionary_id=3223; lemma=sort; gloss=kind, sort); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** rod: Broadly intelligible but highly polysemous.; tip: Reserved here for the typing operation and liable to collapse sort/type distinctions. - **Neizvěstnost / uncertainty:** National formal-logic traditions often use type or kind cognates alongside sort. ## OLISV-T0232 · logic.sort-typed - **English lemma / sense:** sort-typed — Constrained by a profile of input and output sorts, especially for functions and relations in a many-sorted language. - **Medžuslovjansky:** `tipizovany`; lemma `tipizovany`; hard passive adjective. - **Upotrěbljenje / inflection:** Use tipizovana funkcija and tipizovano odnošenje; specify the profile with sortami or a genitive complement. - **Kirilična forma:** `типизованы` - **Argumentacija / rationale:** A single adjective covers typed functions and relations without multiplying compositional heads; context supplies the sort profile. - **Uvěrjenost / status:** 0.73 (medium); `provisional`; revision `OLISV-T0232-r0001`. - **Slovjanske sravnenja / comparanda:** ru: типизированный по сортам; uk: типізований за сортами; pl: typowany według sortów; cs: typovaný podle sortů; bcs: tipiziran prema sortama; типизиран према сортама; bg: типизиран по сортове. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[17844]; dictionary_id=3224; lemma=tip; gloss=type, kind); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** sortovany: Normally suggests sorting or ordering rather than assignment of a formal type profile.; tipovy: Does not clearly express that the object has been constrained by a profile. - **Neizvěstnost / uncertainty:** No direct frozen tipizovany headword was found; national usage varies between typed and sorted terminology. ## OLISV-T0147 · logic.subformula - **English lemma / sense:** subformula — A formula occurring as a component of a larger formula, including the formula itself under the source's reflexive convention. - **Medžuslovjansky:** `podformula`; lemma `podformula`; feminine noun. - **Upotrěbljenje / inflection:** Genitive podformuly; use the same head for a formula contained in another formula and for the reflexive convention stated by the source. - **Kirilična forma:** `подформула` - **Argumentacija / rationale:** Podformula is a transparent pod- compound over the canonical formula head. It preserves the source's technical distinction from a general symbol-string substring while remaining readable across the six comparison traditions. - **Uvěrjenost / status:** 0.78 (medium); `provisional`; revision `OLISV-T0147-r0001`. - **Slovjanske sravnenja / comparanda:** ru: подформула; uk: підформула; pl: podformuła; cs: podformule; bcs: podformula; подформула; bg: подформула. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-DICT-LIVE-20260825 (wordList[7255]; dictionary_id=5181); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** podniz formula: Podniz is already used for a contiguous substring of a symbol string; importing it here would blur the source's formula-level containment relation. - **Neizvěstnost / uncertainty:** The frozen dictionary has no direct specialist podformula head; the term is a compositional edition choice.; National traditions vary between podformula and podstruka/podłańcuch-like compounds; the source fixes the formula-level sense.; No official or native certification is claimed for the complete specialist compound. ## OLISV-T0075 · logic.substitution - **English lemma / sense:** substitution — The recursive operation that replaces every occurrence of x in a term by t, and—when t is admissible for x in A—replaces all free occurrences of x in a formula A by t without variable capture. - **Medžuslovjansky:** `podstanovka`; lemma `podstanovka`; feminine noun. - **Upotrěbljenje / inflection:** Use podstanovka terma t vměsto prěměnnoj x. In a term it replaces every occurrence of x; in a formula it replaces all free occurrences only when t možno podstaviti vměsto x without capture. Generic zaměniti remains explanatory prose. - **Kirilična forma:** `подстановка` - **Argumentacija / rationale:** Podstanovka preserves exact inherited mathematical usage and the accepted Open Logic introduction. OLP-0158 now distinguishes the two recursive branches precisely: all occurrences in a term, but all free occurrences in a formula under the free-for condition. This append-only revision corrects the earlier compressed sense without changing the preferred head. - **Uvěrjenost / status:** 0.78 (medium); `provisional`; revision `OLISV-T0075-r0002`. - **Slovjanske sravnenja / comparanda:** ru: подстановка; замена; uk: підстановка; заміна; pl: podstawienie; zastępstwo; cs: substituce; záměna; bcs: supstitucija; zamjena; bg: подстановка; замяна. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[14249-14253], wordList[16508]; dictionary_id=3810,3811,19420,19421,1627,36101; lemma=zaměnjati, zaměniti, zastųpati, zastųpiti, zaměna); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** zaměna: Directly attested and useful in explanatory prose, but too broad for the recursively defined operation and may also imply exchange or swapping.; substitucija: Internationally recognizable but unsupported as an Interslavic lemma in the registered witnesses and unnecessary given inherited podstanovka. - **Neizvěstnost / uncertainty:** The registered dictionary does not attest podstanovka.; The inherited Noether uses document mathematical substitution but not this exact recursive first-order operation.; No standalone verb entry is created; podstaviti occurs within OLISV-T0156 and accepted explanatory prose. ## OLISV-T0135 · logic.substring - **English lemma / sense:** substring — A contiguous sequence of symbols occurring inside a longer symbol string. - **Medžuslovjansky:** `podniz`; lemma `podniz`; masculine noun. - **Upotrěbljenje / inflection:** Genitive podniza; unlike podposlědovnost, the occurrence must be contiguous. - **Kirilična forma:** `подниз` - **Argumentacija / rationale:** The compact native compound directly encodes containment in a symbol sequence and agrees with South and Bulgarian technical usage. - **Uvěrjenost / status:** 0.72 (medium); `provisional`; revision `OLISV-T0135-r0001`. - **Slovjanske sravnenja / comparanda:** ru: подстрока; uk: підрядок; pl: podłańcuch; cs: podřetězec; bcs: podniz; подниз; bg: подниз. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** podposlědovnost: A subsequence need not be contiguous and therefore changes the source's precise claim. - **Neizvěstnost / uncertainty:** Polish and Czech prefer compounds based on chain/string rather than niz. ## OLISV-T0174 · logic.subterm - **English lemma / sense:** subterm — A term occurring as a constituent within a term or formula whose semantic value contributes compositionally to the value or satisfaction of the containing expression. - **Medžuslovjansky:** `podterm`; lemma `podterm`; masculine noun. - **Upotrěbljenje / inflection:** Genitive plural podtermov. Reserve podizraz for the broader category that can also include subformulas. - **Kirilična forma:** `подтерм` - **Argumentacija / rationale:** Podterm composes the already canonical formal-syntax term with the productive pod- relation and is transparent across the comparison languages. The narrow head avoids conflating a subterm with the broader category of subexpression or subformula. - **Uvěrjenost / status:** 0.74 (medium); `provisional`; revision `OLISV-T0174-r0001`. - **Slovjanske sravnenja / comparanda:** ru: подтерм; uk: підтерм; pl: podterm; cs: podterm; bcs: podterm; подтерм; bg: подтерм. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[17056]; dictionary_id=2091; term root); ISV-DICT-LIVE-20260825 (wordList[17915], wordList[17919]; dictionary_id=4933,737; pod component); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** podizraz: Broader than the source: it can denote a subexpression or subformula rather than specifically a constituent term.; subterm: The unadapted Latin prefix is less immediately transparent across Slavic readers than the productive pod- compound. - **Neizvěstnost / uncertainty:** No direct Interslavic dictionary headword for the complete formal-logic compound was found in the pinned response.; The cross-Slavic surfaces are transparent editorial comparanda rather than a claim of uniform national-corpus preference. ## OLISV-T0124 · logic.symbol - **English lemma / sense:** symbol — A basic written token in the alphabet of a formal language. - **Medžuslovjansky:** `simbol`; lemma `simbol`; masculine noun. - **Upotrěbljenje / inflection:** Genitive simbola; distinguish symbol type from a particular printed occurrence where necessary. - **Kirilična forma:** `симбол` - **Argumentacija / rationale:** Direct lemma and virtually identical national forms give maximal accessibility. - **Uvěrjenost / status:** 0.96 (high); `provisional`; revision `OLISV-T0124-r0001`. - **Slovjanske sravnenja / comparanda:** ru: символ, знак; uk: символ, знак; pl: symbol; cs: symbol, znamení; bcs: simbol; симбол, знак, лик, слика; bg: символ, знак. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[16812]; dictionary_id=12221); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** znak: Znak remains a useful synonym but is broader and can denote signs, values, or marks. - **Neizvěstnost / uncertainty:** The dictionary also glosses token; Open Logic supplies the formal-language restriction. ## OLISV-T0143 · logic.symbol-occurrence - **English lemma / sense:** symbol occurrence — One token-position at which a particular symbol appears in a written formula or symbol string. - **Medžuslovjansky:** `pojavjenje simbola`; lemma `pojavjenje simbola`; neuter noun phrase. - **Upotrěbljenje / inflection:** Genitive pojavjenja simbola; count separate token positions even when the printed symbol type is the same. - **Kirilična forma:** `појавјење симбола` - **Argumentacija / rationale:** A normalized appearance noun plus canonical simbol is broadly readable and lets the text distinguish the first and second occurrence of the same connective. - **Uvěrjenost / status:** 0.8 (medium); `provisional`; revision `OLISV-T0143-r0001`. - **Slovjanske sravnenja / comparanda:** ru: вхождение символа; uk: входження символу; pl: wystąpienie symbolu; cs: výskyt symbolu; bcs: pojava simbola; појава симбола; bg: срещане на символ. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[965]; dictionary_id=10818); ISV-DICT-LIVE-20260825 (wordList[16812]; dictionary_id=12221); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** pojava simbola: The shorter noun is transparent in South Slavic but less directly aligned with the frozen Interslavic derivational head. - **Neizvěstnost / uncertainty:** The dictionary's general appearance sense is specialized here to token occurrence by the Open Logic locus. ## OLISV-T0133 · logic.symbol-string - **English lemma / sense:** string of symbols — A finite ordered sequence of symbol occurrences treated as a syntactic object. - **Medžuslovjansky:** `niz simbolov`; lemma `niz simbolov`; masculine noun phrase. - **Upotrěbljenje / inflection:** Genitive niza simbolov; use niz only for the formal ordered-sequence sense in this context. - **Kirilična forma:** `низ симболов` - **Argumentacija / rationale:** The native sequence head is maximally transparent in South Slavic and remains legible through the wider Slavic sequence vocabulary; the explicit symbol complement blocks the physical-string sense. - **Uvěrjenost / status:** 0.74 (medium); `provisional`; revision `OLISV-T0133-r0001`. - **Slovjanske sravnenja / comparanda:** ru: строка символов; uk: рядок символів; pl: ciąg symboli; cs: řetězec symbolů; bcs: niz simbola; низ симбола; bg: низ от символи. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[16812]; dictionary_id=12221); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** struna simbolov: A literal string cognate denotes cord or an instrument string in the frozen dictionary and is unsuitable for the formal object. - **Neizvěstnost / uncertainty:** The noun niz is an editorial technical extension rather than a direct frozen dictionary headword. ## OLISV-T0132 · logic.syntactic-identity - **English lemma / sense:** syntactic identity — Exact token-by-token identity of two symbol strings, independent of semantic equivalence. - **Medžuslovjansky:** `sintaktična identičnost`; lemma `sintaktična identičnost`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive sintaktičnoj identičnosti; reserve identičnost alone for the broader logical relation and never substitute semantic equivalence. - **Kirilična forma:** `синтактична идентичност` - **Argumentacija / rationale:** The compound specializes the established identity term with an internationally convergent syntactic modifier. - **Uvěrjenost / status:** 0.86 (high); `provisional`; revision `OLISV-T0132-r0001`. - **Slovjanske sravnenja / comparanda:** ru: синтаксическое тождество; uk: синтаксична тотожність; pl: identyczność syntaktyczna; cs: syntaktická totožnost; bcs: sintaktički identitet; синтаксички идентитет; bg: синтактична тъждественост. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[8849]; dictionary_id=35748); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** tekstualna ravnost: The alternative is less precise about token identity and risks confusion with mathematical equality. - **Neizvěstnost / uncertainty:** The exact compound is editorial rather than a direct dictionary row. ## OLISV-T0091 · logic.syntax - **English lemma / sense:** syntax — Rules governing the well-formed expressions of a formal language. - **Medžuslovjansky:** `sintaksa`; lemma `sintaksa`; feminine noun. - **Upotrěbljenje / inflection:** Use genitive sintaksy; distinguish formal syntax from grammar of a natural language. - **Kirilična forma:** `синтакса` - **Argumentacija / rationale:** Direct international lemma with complete East, West, and South Slavic convergence. - **Uvěrjenost / status:** 0.94 (high); `provisional`; revision `OLISV-T0091-r0001`. - **Slovjanske sravnenja / comparanda:** ru: синтаксис; uk: синтаксис; pl: syntaksa, składnia; cs: syntaxe; bcs: sintaksa; синтакса, структура (реченице); bg: синтаксис. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[16835]; dictionary_id=3140); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** skladnja: The West-Slavic native alternative is less broadly transparent than the international form. - **Neizvěstnost / uncertainty:** The dictionary sense is general syntax; Open Logic supplies the formal-logical restriction. ## OLISV-T0313 · logic.temporal - **English lemma / sense:** temporal logic — A modal application in which Box A may mean that A is always true and Diamond A that A is sometimes true. - **Medžuslovjansky:** `temporalna logika`; lemma `temporalna logika`; feminine adjective-noun phrase. - **Upotrěbljenje / inflection:** Feminine logika; genitive temporalnoj logiky. - **Kirilična forma:** `темпорална логика` - **Argumentacija / rationale:** Temporalna logika retains the internationally searchable temporal label and the source's always/sometimes contrast. It is accompanied by the source definition rather than overclaiming a particular branching-time semantics. - **Uvěrjenost / status:** 0.86 (high); `provisional`; revision `OLISV-T0313-r0001`. - **Slovjanske sravnenja / comparanda:** ru: временная логика; uk: темпоральна логіка; pl: logika temporalna; cs: temporální logika; bcs: vremenska logika; bg: темпорална логика. - **Dokazy / evidence:** OL-FOL-BEYOND-MODAL-LOGICS (lines 63-64); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** časova logika: The native time adjective can suggest ordinary chronology and is less stable across the six comparison languages than the transparent international temporal form. - **Neizvěstnost / uncertainty:** The source leaves tense, direction, and branching structure underspecified; this entry names the application class only. ## OLISV-T0095 · logic.term - **English lemma / sense:** term — A first-order syntactic expression denoting an object once interpreted. - **Medžuslovjansky:** `term`; lemma `term`; masculine noun. - **Upotrěbljenje / inflection:** Genitive singular terma; do not confuse this formal category with termin as a deadline or lexical term. - **Kirilična forma:** `терм` - **Argumentacija / rationale:** Term is already entrenched by termovy model and značenje terma and sharply separates the formal category from termin's competing senses. - **Uvěrjenost / status:** 0.68 (medium); `provisional`; revision `OLISV-T0095-r0001`. - **Slovjanske sravnenja / comparanda:** ru: терм; uk: терм; pl: term; cs: term; bcs: term; bg: терм. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[17056]; dictionary_id=2091); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** termin: The direct dictionary form is broad and also denotes a date or lexical designation; it is retained as adverse evidence. - **Neizvěstnost / uncertainty:** The preferred root is an edition-level specialist normalization rather than a direct dictionary headword. ## OLISV-T0273 · logic.theorem - **English lemma / sense:** theorem — A mathematical statement presented with a proof or as a result to be proved. - **Medžuslovjansky:** `teorema`; lemma `teorema`; feminine noun. - **Upotrěbljenje / inflection:** Feminine teorema; plural teoremy, genitive teoremy. - **Kirilična forma:** `теорема` - **Argumentacija / rationale:** Teorema is the transparent international mathematical head already used by the target. The source's theorem environments fix the proved-result sense, while the statement row supplies only the semantic class. - **Uvěrjenost / status:** 0.91 (high); `provisional`; revision `OLISV-T0273-r0001`. - **Slovjanske sravnenja / comparanda:** ru: теорема; uk: теорема; pl: twierdzenie; cs: věta; bcs: teorem; теорема; bg: теорема. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 42-47 and 117-126); ISV-DICT-LIVE-20260825 (dictionary_id=1087; lemma=tvŕđeńje; gloss=statement, claim, assertion); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** dokazano tvrdženje: A descriptive paraphrase obscures the conventional theorem category and its environment label. - **Neizvěstnost / uncertainty:** The pinned dictionary has no direct teorema head; the selection is source- and cross-Slavic rather than dictionary-certified. ## OLISV-T0371 · logic.theory-incompleteness - **English lemma / sense:** incompleteness — The failure of a sufficiently strong consistent formal theory to decide every sentence, here manifested by its consistency sentence and negation. - **Medžuslovjansky:** `nepolnota`; lemma `nepolnota`; feminine abstract noun. - **Upotrěbljenje / inflection:** Feminine noun nepolnota; genitive nepolnoty. Use teorema nepolnoty for an incompleteness theorem and nepolny for the adjective. - **Kirilična forma:** `неполнота` - **Argumentacija / rationale:** Nepolnota is the regular negative counterpart of the established canon head polnota (OLISV-T0061). It aligns exactly with Russian and closely with Ukrainian, Czech, Croatian, Polish, and Bulgarian negative full/complete families while keeping the formal-theory sense fixed by the Open Logic explanation. - **Uvěrjenost / status:** 0.88 (high); `provisional`; revision `OLISV-T0371-r0001`. - **Slovjanske sravnenja / comparanda:** ru: неполнота; uk: неповнота; pl: niezupełność; cs: neúplnost; bcs: nepotpunost; bg: непълнота. - **Dokazy / evidence:** OL-MODEL-ARITHMETIC-INTRODUCTION (lines 55-64); ISV-DICT-LIVE-20260825 (wordList[3821-3822]; dictionary_id=4378,10922); RU-MSU-GODEL-LECTURES-2020 (title and physical page 8 / extracted lines 395-402); CS-CUNI-LOGIC-II-2008 (physical page 1 / extracted lines 28 and 33-45); HR-ZAGREB-CLASSICAL-LOGIC-2013 (chapter title and physical pages 66-69 / extracted lines 35-57); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic, standard flavorization) - **Alternativy / alternatives:** nekompletnost: The international complete stem is recognizable but would break the established polnota family and is less directly aligned with the strongest native Slavic comparanda.; nepopolnost: It mirrors one dictionary completeness derivative more mechanically, but the accepted edition already uses polnota and the shorter negative form is more stable in current prose. - **Neizvěstnost / uncertainty:** The exact selected surface is an edition-level derivation from OLISV-T0061 rather than a direct pinned dictionary lemma.; Polish and Bulgarian national surfaces in this packet are transparent derivations rather than direct academic attestations. ## OLISV-T0013 · logic.truth - **English lemma / sense:** truth — The semantic property of being true, including the truth constant and logical truth. - **Medžuslovjansky:** `istina`; lemma `istina`; feminine noun. - **Upotrěbljenje / inflection:** Feminine abstract noun; genitive singular istiny. Use logična istina for logical truth and cěnnost istiny only where a truth-value phrase is intended. - **Kirilična forma:** `истина` - **Argumentacija / rationale:** Istina avoids the justice-related ambiguity of pravda in formal semantics and matches East and South Slavic terminology; the dictionary row explicitly records the West Slavic pravda comparanda. - **Uvěrjenost / status:** 0.88 (high); `seed_preferred`; revision `OLISV-T0013-r0001`. - **Slovjanske sravnenja / comparanda:** ru: истина; uk: істина; pl: prawda; cs: pravda; bcs: istina; bg: истина. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[17697]; dictionary_id=7935); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** pravda: Although more immediately transparent to West Slavs and a type-1 dictionary lemma, pravda also denotes justice; istina is more sense-specific for semantics. - **Neizvěstnost / uncertainty:** West Slavic readers may find pravda more immediate; the selected istina is a deliberate semantic-disambiguation choice. ## OLISV-T0120 · logic.truth-functional-completeness - **English lemma / sense:** truth-functional completeness — The property that a set of Boolean operators can express every truth function. - **Medžuslovjansky:** `istinnostno-funkcionalna polnota`; lemma `istinnostno-funkcionalna polnota`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive istinnostno-funkcionalnoj polnoty; apply to an operator set or basis, not an arbitrary proof system. - **Kirilična forma:** `истинностно-функционална полнота` - **Argumentacija / rationale:** The compound reuses the canonical polnota while spelling out the truth-functional restriction. - **Uvěrjenost / status:** 0.78 (medium); `provisional`; revision `OLISV-T0120-r0001`. - **Slovjanske sravnenja / comparanda:** ru: функциональная полнота; uk: функціональна повнота; pl: zupełność funkcjonalna; cs: funkční úplnost; bcs: funkcionalna potpunost; функционална потпуност; bg: функционална пълнота. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** funkcionalna polnota: The shorter form can be misread as completeness for arbitrary mathematical functions. - **Neizvěstnost / uncertainty:** The exact compound is editorial and not a direct dictionary lemma. ## OLISV-T0159 · logic.truth-table - **English lemma / sense:** truth table — A finite table recording the resulting truth value of a truth-functional connective or formula for every possible combination of input truth values. - **Medžuslovjansky:** `tabela istinnosti`; lemma `tabela istinnosti`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive singular tabely istinnosti; plural tabely istinnosti. Istinnosti remains a fixed genitive complement. - **Kirilična forma:** `табела истинности` - **Argumentacija / rationale:** Tabela is the data-table head directly selected by the frozen Interslavic dictionary. Istinnosti preserves the already canonical istina and istinnostno-funkcionalna family while avoiding the truth/justice ambiguity of pravda. The compound is transparent across Slavic readers and is explicitly bounded as an editorial specialist formation. - **Uvěrjenost / status:** 0.72 (medium); `provisional`; revision `OLISV-T0159-r0001`. - **Slovjanske sravnenja / comparanda:** ru: таблица истинности; uk: таблиця істинності; pl: tablica prawdy; cs: pravdivostní tabulka; bcs: tablica istinitosti; таблица истинитости; bg: таблица на истинност. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[16851]; dictionary_id=12884; lemma=tabela; gloss=table (data), spreadsheet); ISV-DICT-LIVE-20260825 (wordList[17697]; dictionary_id=7935; lemma=istina; gloss=truth); ISV-DICT-LIVE-20260825 (wordList[13965]; dictionary_id=5108; lemma=istinnosť; gloss=reality, truthfulness); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** tabela istiny: Compositionally possible, but less conventional for a technical relation than the established istinnost- derivational family.; tabela pravdy: West-readable, but pravda carries the truth/justice ambiguity already avoided by the edition's canonical truth family.; tablica istinnosti: National support exists, but the frozen Interslavic dictionary directly selects tabela for a data table. - **Neizvěstnost / uncertainty:** The complete Interslavic compound is editorial rather than a direct dictionary lemma.; National traditions divide between istina-, istinnost-, pravda-, and pravdivost-family constructions.; No native or official certification is claimed for the complete phrase. ## OLISV-T0258 · logic.truth-value - **English lemma / sense:** truth value — An object of the distinguished type Omega representing true or false in the higher-order language. - **Medžuslovjansky:** `cěnnost istiny`; lemma `cěnnost istiny`; feminine noun phrase. - **Upotrěbljenje / inflection:** Feminine cěnnost; genitive cěnnosti istiny. In the target prose use cěnnostij istiny after the instrumental preposition. - **Kirilična forma:** `цєнност истины` - **Argumentacija / rationale:** Cěnnost istiny reuses the established truth-value phrase. The value and truth components are directly pinned, while the source's Omega true/false interpretation fixes the specialist sense. - **Uvěrjenost / status:** 0.94 (high); `provisional`; revision `OLISV-T0258-r0002`. - **Slovjanske sravnenja / comparanda:** ru: значение истинности; uk: значення істинності; pl: wartość logiczna; cs: pravdivostní hodnota; bcs: istinosna vrijednost; истинска вредност; bg: стойност на истинност. - **Dokazy / evidence:** OL-FOL-BEYOND-HIGHER-ORDER-LOGIC (lines 32-38 and 95-100); ISV-DICT-LIVE-20260825 (dictionary_id=2281; lemma=cěnnosť; gloss=value); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3); ISV-DICT-LIVE-20260825 (dictionary_id=7935; lemma=istina; gloss=truth) - **Alternativy / alternatives:** istinnost: Names truth-functional behavior or truthiness and is already used in a different canon entry.; vrědnost istiny: The vrěd family is not the pinned dictionary head for value and would introduce an unsupported variant. - **Neizvěstnost / uncertainty:** The direct dictionary value row is spelled cěnnosť; the edition's cěnnost surface is a documented normalized form.; The established T0013 truth-value lineage is reused; this record does not treat tip as a lexical component.; The r0001 record is preserved as adverse provenance for the evidence correction. ## OLISV-T0256 · logic.type - **English lemma / sense:** type — A syntactic label classifying the objects over which higher-order terms and variables range. - **Medžuslovjansky:** `tip`; lemma `tip`; masculine noun. - **Upotrěbljenje / inflection:** Masculine tip; plural tipy, genitive tipa. Keep the head distinct from sort when the source explicitly uses higher-order types. - **Kirilična forma:** `тип` - **Argumentacija / rationale:** Tip is a direct dictionary lemma and the source explicitly introduces it as the replacement for the informal sort labels. The dedicated entry fixes the higher-order syntactic sense while preserving the broader everyday kind sense in the dictionary. - **Uvěrjenost / status:** 0.96 (high); `provisional`; revision `OLISV-T0256-r0002`. - **Slovjanske sravnenja / comparanda:** ru: тип; uk: тип; pl: typ; cs: typ; bcs: tip; тип; bg: тип. - **Dokazy / evidence:** OL-FOL-BEYOND-HIGHER-ORDER-LOGIC (lines 21-32); ISV-DICT-LIVE-20260825 (dictionary_id=3224; lemma=tip; gloss=type, kind); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** sort: Sort is retained for the earlier many-sorted vocabulary, but would erase the source's deliberate type/sort distinction. - **Neizvěstnost / uncertainty:** The word tip is polysemous in general language; the source context supplies the specialist restriction.; The r0001 record is preserved as adverse provenance for the evidence correction. ## OLISV-T0321 · logic.uncertainty - **English lemma / sense:** uncertainty — Lack of determinate information or outcome that the source assigns as the reasoning target of probabilistic logic. - **Medžuslovjansky:** `neoprěděljenost`; lemma `neoprěděljenost`; feminine abstract noun. - **Upotrěbljenje / inflection:** Feminine abstract noun; genitive and locative neoprěděljenosti. - **Kirilična forma:** `неопрєдєљеност` - **Argumentacija / rationale:** Neoprěděljenost denotes objective indeterminacy and thereby fits the probabilistic source context better than a form centered on a person's lack of confidence. The -ost derivation is regular and broadly recognizable. - **Uvěrjenost / status:** 0.86 (high); `provisional`; revision `OLISV-T0321-r0001`. - **Slovjanske sravnenja / comparanda:** ru: неопределённость; uk: невизначеність; pl: niepewność; nieokreśloność; cs: neurčitost; bcs: neodređenost; неодређеност; bg: неопределеност. - **Dokazy / evidence:** OL-FOL-BEYOND-OTHER-LOGICS (lines 24-25); ISV-DICT-LIVE-20260825 (dictionary_id=9609; lemma=neoprěděljeny; gloss=indefinite, indeterminate); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** neuvěrjenost: This would foreground being personally unsure and is narrower than the source's general uncertainty modeled by probabilistic logic. - **Neizvěstnost / uncertainty:** The source does not distinguish aleatory from epistemic uncertainty; the term intentionally remains at that general level. ## OLISV-T0104 · logic.unique-readability - **English lemma / sense:** unique readability — The property that every well-formed expression has a unique parse under the formation rules. - **Medžuslovjansky:** `jednoznačna čitljivost`; lemma `jednoznačna čitljivost`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive jednoznačnoj čitljivosti; treat as a parsing theorem, not an automatic consequence of induction. - **Kirilična forma:** `једнозначна читљивост` - **Argumentacija / rationale:** The descriptive native phrase is transparent and mirrors the established theorem label in the translated propositional corpus. - **Uvěrjenost / status:** 0.71 (medium); `provisional`; revision `OLISV-T0104-r0001`. - **Slovjanske sravnenja / comparanda:** ru: однозначная читаемость; uk: однозначна читаність; pl: jednoznaczna czytelność; cs: jednoznačná čitelnost; bcs: jednoznačna čitljivost; једнозначна читљивост; bg: еднозначна четимост. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** unikalna čitljivost: Unikalna can suggest mere distinctness rather than a unique structural parse. - **Neizvěstnost / uncertainty:** No direct frozen dictionary row attests the specialist phrase.; The English source understates the extra delimiter and arity assumptions needed for the theorem. ## OLISV-T0158 · logic.universal-instance - **English lemma / sense:** instance of a universally quantified formula — The formula A(t), defined as the substitution result Subst(A,t,x) for an admissible term t, regarded as a syntactic instance of the universally quantified formula forall x A(x). - **Medžuslovjansky:** `podstanovny slučaj`; lemma `podstanovny slučaj`; masculine noun phrase. - **Upotrěbljenje / inflection:** Genitive podstanovnogo slučaja. Use only for the admissible substituted formula A(t), not for an arbitrary example or semantic model instance. - **Kirilična forma:** `подстановны случај` - **Argumentacija / rationale:** Slučaj is directly glossed with case and instance across the frozen dictionary, while podstanovny restricts it to the source's precise syntactic construction. The compound is more transparent across Slavic readers than an unattested international loan. - **Uvěrjenost / status:** 0.64 (medium); `provisional`; revision `OLISV-T0158-r0001`. - **Slovjanske sravnenja / comparanda:** ru: частный случай универсальной формулы; uk: частковий випадок універсальної формули; pl: instancja formuły ogólnej; cs: instance univerzální formule; bcs: slučaj univerzalne formule; случај универзалне формуле; bg: частен случай на универсална формула. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-DICT-LIVE-20260825 (wordList[2999]; dictionary_id=1333); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** priměr: Priměr names an example and does not assert the formal substitution relation to a universally quantified formula.; slučaj: Directly attested and retained as the head component, but too broad alone to identify the admissibly substituted A(t) construction.; instancija: Internationally recognizable in some national traditions but unattested in the frozen Interslavic dictionary and less transparent across all three Slavic zones. - **Neizvěstnost / uncertainty:** The frozen dictionary directly supports only generic slučaj, not podstanovny slučaj.; National traditions alternate between instance and particular-case terminology.; No native or official certification is claimed for the complete compound. ## OLISV-T0117 · logic.universal-quantifier - **English lemma / sense:** universal quantifier — A quantifier asserting that its scope holds for every domain object. - **Medžuslovjansky:** `universalny kvantifikator`; lemma `universalny kvantifikator`; masculine noun phrase. - **Upotrěbljenje / inflection:** Genitive universalnogo kvantifikatora; associated with the forall symbol. - **Kirilična forma:** `универсалны квантификатор` - **Argumentacija / rationale:** International modifier plus canonical quantifier is immediately recognizable in every comparison language. - **Uvěrjenost / status:** 0.89 (high); `provisional`; revision `OLISV-T0117-r0001`. - **Slovjanske sravnenja / comparanda:** ru: квантор всеобщности; uk: квантор загальності; pl: kwantyfikator ogólny; cs: obecný kvantifikátor; bcs: univerzalni kvantifikator; универзални квантификатор; bg: квантор за всеобщност. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** občny kvantifikator: The native adjective can suggest generality without the precise all-objects force. - **Neizvěstnost / uncertainty:** The complete compound is not a direct frozen dictionary headword. ## OLISV-T0315 · logic.universal-relation - **English lemma / sense:** universal relation — A relation holding from every world to every other world, used in the source's S5 frame description. - **Medžuslovjansky:** `universalno odnošenje`; lemma `universalno odnošenje`; neuter adjective-noun phrase. - **Upotrěbljenje / inflection:** Neuter odnošenje; genitive universalnogo odnošenja. Preserve the source's every-world consequence and its pedagogical boundary. - **Kirilična forma:** `универсално одношење` - **Argumentacija / rationale:** Universalno odnošenje directly composes the universal adjective and relation head and mirrors the source's explicit explanation that every world is accessible from every other. The canon flags the standard S5 equivalence nuance as adverse evidence instead of silently rewriting the source. - **Uvěrjenost / status:** 0.9 (high); `provisional`; revision `OLISV-T0315-r0001`. - **Slovjanske sravnenja / comparanda:** ru: универсальное отношение; uk: універсальне відношення; pl: relacja uniwersalna; cs: univerzální relace; bcs: univerzalna relacija; bg: универсално отношение. - **Dokazy / evidence:** OL-FOL-BEYOND-MODAL-LOGICS (lines 84-89); ISV-DICT-LIVE-20260825 (dictionary_id=3072; lemma=universaľny; gloss=universal); ISV-DICT-LIVE-20260825 (dictionary_id=1992; lemma=odnošeńje; gloss=relation); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** ekvivalenčno odnošenje: An equivalence relation is a common standard-frame characterization, but replacing the source's universal wording would erase a meaningful pedagogical claim and its exact truth consequence. - **Neizvěstnost / uncertainty:** The source's universal relation is a pedagogical simplification of standard S5 frame conditions; no claim is made that the source exhausts the model-theoretic theory. ## OLISV-T0319 · logic.vague-property - **English lemma / sense:** vague property — A property whose applicability is not sharply determined, forming the target of the source's fuzzy-logic example. - **Medžuslovjansky:** `nejasno svojstvo`; lemma `nejasno svojstvo`; neuter adjective-noun phrase. - **Upotrěbljenje / inflection:** Neuter svojstvo; genitive nejasnogo svojstva and plural nejasne svojstva. - **Kirilična forma:** `нејасно својство` - **Argumentacija / rationale:** Nejasno svojstvo directly composes the frozen vague and property lemmas and remains understandable without prior familiarity with fuzzy-logic jargon. The bounded source fixes vagueness, not general semantic ambiguity. - **Uvěrjenost / status:** 0.93 (high); `provisional`; revision `OLISV-T0319-r0001`. - **Slovjanske sravnenja / comparanda:** ru: неясное свойство; uk: нечітка властивість; pl: niejasna własność; cs: vágní vlastnost; bcs: nejasno svojstvo; нејасно својство; bg: неясно свойство. - **Dokazy / evidence:** OL-FOL-BEYOND-OTHER-LOGICS (lines 23-24); ISV-DICT-LIVE-20260825 (dictionary_id=35264; lemma=nejasny; gloss=unclear, vague); ISV-DICT-LIVE-20260825 (dictionary_id=22019; lemma=svojstvo; gloss=characteristic, property); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** razmyto svojstvo: The blur metaphor is useful for the logic's name, but the direct nejasny lemma more exactly denotes the source's property-level vagueness. - **Neizvěstnost / uncertainty:** Vagueness, ambiguity, and uncertainty are distinct technical notions; this entry is limited to the source's vague-property wording. ## OLISV-T0071 · logic.validity - **English lemma / sense:** validity — A formula's holding under every interpretation admitted by the semantics: truth in every classical structure, or forcing at every relevant world of every intuitionistic Kripke structure. - **Medžuslovjansky:** `validnost`; lemma `validnost`; feminine abstract noun. - **Upotrěbljenje / inflection:** Use validny for the adjective and distinguish validity from truth in one particular structure. - **Kirilična forma:** `валидност` - **Argumentacija / rationale:** Validnost extends an already frequent and unambiguous inherited mathematical adjective into the precisely defined logical property. It is broadly international and avoids the registered legal sense of pravomoćny; the Open Logic source keeps validity distinct from truth relative to one structure. The dedicated OLP-0179 unit now broadens the current sense while the earlier revision remains preserved as scope provenance. - **Uvěrjenost / status:** 0.82 (high); `provisional`; revision `OLISV-T0071-r0002`. - **Slovjanske sravnenja / comparanda:** ru: общезначимость; валидность; uk: загальнозначущість; валідність; pl: ważność logiczna; cs: logická platnost; bcs: validnost; valjanost; bg: логическа валидност; общовалидност. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 180-184 and 220-222); ISV-DICT-LIVE-20260825 (wordList[18216]; dictionary_id=37979; lemma=pravomoćny; gloss=valid, legally binding); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** pravomoćnost: The registered family is expressly legal and would misstate the logical sense.; občeistinnost: Compositionally suggests universal truth but is unattested and needlessly replaces the stable inherited international root. - **Neizvěstnost / uncertainty:** The registered dictionary does not directly list validnost in the logical sense.; National traditions divide between international valid- and native universal-validity formations.; Earlier narrower sense wording remains preserved in the superseded revision. ## OLISV-T0094 · logic.variable - **English lemma / sense:** variable — A syntactic symbol whose semantic value is supplied by an assignment. - **Medžuslovjansky:** `prěměnna`; lemma `prěměnna`; feminine noun. - **Upotrěbljenje / inflection:** Genitive singular prěměnnoj; reserve the adjectival prěměnny for varying objects. - **Kirilična forma:** `прємєнна` - **Argumentacija / rationale:** The noun is directly listed and bridges East/West native traditions while remaining legible in the South. - **Uvěrjenost / status:** 0.91 (high); `provisional`; revision `OLISV-T0094-r0001`. - **Slovjanske sravnenja / comparanda:** ru: переменная; uk: змінна; pl: zmienna; cs: proměnná; bcs: varijabla; променљива; bg: променлива. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[18234]; dictionary_id=35526); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** varijabla: The international South-Slavic form is less transparent to East and West Slavic readers. - **Neizvěstnost / uncertainty:** Croatian commonly prefers varijabla, recorded in the comparanda. ## OLISV-T0073 · logic.variable-assignment - **English lemma / sense:** variable assignment — A function that assigns a domain value to every variable for evaluating formulas in a structure. - **Medžuslovjansky:** `prisvajanje prěměnnyh`; lemma `prisvajanje prěměnnyh`; neuter noun phrase. - **Upotrěbljenje / inflection:** The short technical term denotes the whole value-assigning function; expand on first use as prisvajanje cěnnostij prěměnnym when the mapping direction needs emphasis. - **Kirilična forma:** `присвајање прємєнных` - **Argumentacija / rationale:** Prisvajanje prěměnnyh is retained as the short edition term because it is already used throughout the active semantic translation and its cognate assignment family is recognizable across East and South Slavic as well as Polish przypisanie. The definition fixes the technical function sense and prevents the dictionary's appropriation reading. - **Uvěrjenost / status:** 0.62 (medium); `provisional`; revision `OLISV-T0073-r0001`. - **Slovjanske sravnenja / comparanda:** ru: присваивание значений переменным; оценка переменных; uk: присвоєння значень змінним; оцінка змінних; pl: przypisanie wartości zmiennym; wartościowanie; cs: přiřazení hodnot proměnným; ohodnocení; bcs: dodjeljivanje vrijednosti varijablama; bg: присвояване на стойности на променливите. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[1258]; dictionary_id=4229; lemma=pridělańje; gloss=assignment); ISV-DICT-LIVE-20260825 (wordList[1008-1009], wordList[1014]; dictionary_id=22021,22022,36496; lemma=prisvojiti, prisvajati, prisvojeńje); ISV-DICT-LIVE-20260825 (wordList[18234]; dictionary_id=35526; lemma=prěměnna; gloss=variable); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** priděljenje prěměnnyh: The noun is directly listed for assignment but its South Slavic columns emphasize a task or mission, making the unexpanded short phrase less precise for semantic evaluation.; prirěčenje prěměnnyh: It occurs in earlier accepted proof prose but has weaker direct lexical support and is less recognizable to East Slavic readers; it remains adverse history rather than a silent synonym. - **Neizvěstnost / uncertainty:** The selected short term is not directly attested in the registered dictionary's technical sense.; Earlier accepted units use prirěčenje or related forms and require a later bounded canon-reconciliation pass. ## OLISV-T0157 · logic.variable-capture - **English lemma / sense:** variable capture — Unintended binding by a quantifier in A of a variable occurrence that was free in a term t before t was substituted into A. - **Medžuslovjansky:** `zahvat prěměnnoj`; lemma `zahvat prěměnnoj`; masculine noun phrase. - **Upotrěbljenje / inflection:** Genitive zahvata prěměnnoj. Use zahvatiti or zahvaćati only when the unintended binding event is explicit; ordinary binding remains svezanje or svęzanje in reader prose. - **Kirilična forma:** `захват прємєнној` - **Argumentacija / rationale:** Zahvat gives the accidental binding phenomenon a distinct compact head and is directly supported as a take/capture component. Keeping svęzanje for ordinary binding preserves the source's distinction between legitimate scope and unintended capture. - **Uvěrjenost / status:** 0.74 (medium); `provisional`; revision `OLISV-T0157-r0001`. - **Slovjanske sravnenja / comparanda:** ru: захват переменной; uk: захоплення змінної; pl: przechwycenie zmiennej; cs: zachycení proměnné; bcs: hvatanje varijable; хватање променљиве; bg: прихващане на променлива. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-DICT-LIVE-20260825 (wordList[2910]; dictionary_id=571); ISV-DICT-LIVE-20260825 (wordList[2911]; dictionary_id=2292); ISV-DICT-LIVE-20260825 (wordList[2912]; dictionary_id=19363); ISV-DICT-LIVE-20260825 (wordList[18234]; dictionary_id=35526); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** svęzanje prěměnnoj: This collapses accidental capture into ordinary variable binding and therefore loses the source's central warning.; uhvaćenje prěměnnoj: A possible South-Slavic-style capture nominal, but less continuous with the directly registered zahvatiti/zahvaćati/zahvat family. - **Neizvěstnost / uncertainty:** The capture family also has physical seizure or takeover senses outside logic.; West and South Slavic specialist traditions are lexically split.; No native or official certification is claimed for the complete compound. ## OLISV-T0268 · logic.weak-higher-type-semantics - **English lemma / sense:** weak higher-type semantics — A type-indexed semantics with selected domains and application/projection operations rather than all possible functions. - **Medžuslovjansky:** `slabša semantika vyšših tipov`; lemma `slabša semantika vyšših tipov`; feminine noun phrase. - **Upotrěbljenje / inflection:** Feminine semantika; comparative slabša agrees with semantika. Genitive slabšoj semantiky vyšših tipov. - **Kirilična forma:** `слабша семантика вышших типов` - **Argumentacija / rationale:** Slabša preserves the source's explicit weaker-than-full contrast and leaves room for the selected T_tau domains and operations. The phrase is paired with T0267 so the canon records the semantic opposition rather than treating weak as a generic quality adjective. - **Uvěrjenost / status:** 0.91 (high); `provisional`; revision `OLISV-T0268-r0002`. - **Slovjanske sravnenja / comparanda:** ru: слабая семантика высших типов; uk: слабша семантика типів вищого порядку; pl: słabsza semantyka wyższych typów; cs: slabší sémantika vyšších typů; bcs: slabša semantika viših tipova; слабша семантика виших типова; bg: по-слаба семантика на висши типове. - **Dokazy / evidence:** OL-FOL-BEYOND-HIGHER-ORDER-LOGIC (lines 107-112); ISV-DICT-LIVE-20260825 (dictionary_id=1341; lemma=slaby; gloss=weak, feeble); ISV-DICT-LIVE-20260825 (dictionary_id=20302; lemma=vysši; gloss=higher); ISV-DICT-LIVE-20260825 (dictionary_id=3224; lemma=tip; gloss=type, kind); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3); ISV-DICT-LIVE-20260825 (dictionary_id=35935; lemma=semantika; gloss=semantics) - **Alternativy / alternatives:** nepolna semantika: Negation loses the source's ordered strength relation and can suggest an incomplete or defective construction.; ograničena semantika: Would imply an arbitrary restriction rather than the established weaker semantic regime. - **Neizvěstnost / uncertainty:** The comparative slabša is semantically stronger than a bare weak adjective; national traditions may lexicalize the contrast with partial/restricted terms.; The r0001 record is preserved as adverse provenance for the evidence correction. ## OLISV-T0242 · logic.weak-second-order-semantics - **English lemma / sense:** weak second-order semantics — Second-order semantics allowing a sufficiently large but not necessarily full family of relations to satisfy the selected comprehension axioms. - **Medžuslovjansky:** `slabša semantika drugogo reda`; lemma `slabša semantika drugogo reda`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive slabšej semantiky drugogo reda; use slabša semantika for the contrast with full semantics. - **Kirilična forma:** `слабша семантика другого реда` - **Argumentacija / rationale:** Slabša is the established comparative form in the target and preserves the source's contrast between enough relations and all relations. The record keeps completeness claims tied to the weaker semantics rather than silently upgrading them. - **Uvěrjenost / status:** 0.9 (high); `provisional`; revision `OLISV-T0242-r0002`. - **Slovjanske sravnenja / comparanda:** ru: слабая семантика второго порядка; uk: слабка семантика другого порядку; pl: słaba semantyka drugiego rzędu; cs: slabá sémantika druhého řádu; bcs: slabija semantika drugog reda; слабија семантика другог реда; bg: слаба семантика от втори ред. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (dictionary_id=1341; lemma=slaby; gloss=weak, feeble); ISV-DICT-LIVE-20260825 (dictionary_id=35935; lemma=semantika; gloss=semantics); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** nepolna semantika: Negative wording is less transparent and can be mistaken for an incomplete theory.; ograničena semantika: Too broad: the source's defining condition is a relation-family size, not arbitrary restriction. - **Neizvěstnost / uncertainty:** Weak and Henkin terminology differ across national textbooks; the source-bounded label is retained.; The r0001 record remains preserved as adverse provenance for the target/source locator mismatch. ## OLISV-T0167 · logic.x-variant-assignment - **English lemma / sense:** x-variant of a variable assignment — A variable assignment that agrees with a given assignment on every variable except that it may assign a different domain element to the distinguished variable x. - **Medžuslovjansky:** `x-variant prisvajanja`; lemma `x-variant prisvajanja`; masculine noun phrase. - **Upotrěbljenje / inflection:** Variant is masculine: nominative x-variant, instrumental x-variantom. Prisvajanja is a genitive complement. In the Latin head x remains the mathematical symbol; the definition states that the possibly changed value is assigned to x. - **Kirilična forma:** `кс-вариант присвајања` - **Argumentacija / rationale:** X-variant prisvajanja keeps the source's compact, standard model-theoretic label, composes it with the already established OLISV-T0073 variable-assignment term, and uses the directly frozen masculine lemma variant. The definition makes the direction explicit: the possibly different domain value is assigned to x, while all other variable values remain unchanged. - **Uvěrjenost / status:** 0.8 (high); `provisional`; revision `OLISV-T0167-r0001`. - **Slovjanske sravnenja / comparanda:** ru: x-вариант присваивания значений переменным; uk: x-варіант присвоєння значень змінним; pl: x-wariant przypisania wartości zmiennym; cs: x-varianta přiřazení hodnot proměnným; bcs: x-varijanta dodjeljivanja vrijednosti varijablama; bg: x-вариант на присвояването на стойности на променливите. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[18235]; dictionary_id=17059; lemma=variant; partOfSpeech=m.; gloss=variant); ISV-DICT-LIVE-20260825 (wordList[1008-1009], wordList[1014], wordList[18234]; dictionary_id=22021,22022,36496,35526); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** x-varianta prisvajanja: West and South Slavic comparison columns often use a feminine cognate, but the frozen Interslavic dictionary head variant is explicitly masculine; promoting varianta would contradict that direct local evidence.; prisvajanje različajuće se po x: Transparent as explanatory prose but too long for the repeated technical head and less exact about agreement on every other variable; the full definition already provides this explanation.; x-modifikacija prisvajanja: Replaces the source's variant relation with an unsupported modification noun and obscures that the original assignment itself counts as an x-variant. - **Neizvěstnost / uncertainty:** The complete specialist phrase is an edition-level compound rather than a directly listed frozen-dictionary headword.; National comparison traditions differ in the gender and syntax of the variant component; those forms are editorial comparanda, not native certification.; The pinned official Cyrillic projection renders Latin x as кс; mathematical formulas themselves continue to preserve the TeX variable x. ## OLISV-T0276 · mathematics.riemann-hypothesis - **English lemma / sense:** Riemann hypothesis — The named open conjecture used in the source's first constructive-reasoning example. - **Medžuslovjansky:** `Rimanova hipoteza`; lemma `Rimanova hipoteza`; feminine possessive-adjective noun phrase. - **Upotrěbljenje / inflection:** Feminine hipoteza; genitive Rimanovoj hipotezy. Preserve the Riman- proper-name adaptation consistently. - **Kirilična forma:** `Риманова хипотеза` - **Argumentacija / rationale:** Rimanova hipoteza uses the direct hypothesis head and a broadly recognizable Slavic possessive form for the proper name while retaining the source's named referent. - **Uvěrjenost / status:** 0.94 (high); `provisional`; revision `OLISV-T0276-r0001`. - **Slovjanske sravnenja / comparanda:** ru: гипотеза Римана; uk: гіпотеза Рімана; pl: hipoteza Riemanna; cs: Riemannova hypotéza; bcs: Riemannova hipoteza; Риманова хипотеза; bg: хипотеза на Риман. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 19-35); ISV-DICT-LIVE-20260825 (dictionary_id=19517; lemma=hipoteza; gloss=hypothesis); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** hipoteza Rimana: A bare genitive is intelligible but less balanced across West and South Slavic adjective patterns used by the edition. - **Neizvěstnost / uncertainty:** National spellings retain either Riemann or Riman; the single-n adaptation is an edition-level readability choice. ## OLISV-T0201 · mereology.fusion - **English lemma / sense:** mereological fusion — An object composed of specified parts in the source's informal supplementation principle; the unit does not provide a formal definition of fusion. - **Medžuslovjansky:** `mereologična fuzija`; lemma `mereologična fuzija`; feminine noun phrase. - **Upotrěbljenje / inflection:** The adjective agrees with fuzija: genitive mereologičnoj fuzije. In an established mereological context the short form fuzija is permitted. - **Kirilična forma:** `мереологична фузија` - **Argumentacija / rationale:** Mereologična fuzija retains the source's international technical label and is especially transparent in West and South Slavic traditions. The qualification prevents confusion with physical, organizational, or biological fusion. - **Uvěrjenost / status:** 0.78 (medium); `provisional`; revision `OLISV-T0201-r0001`. - **Slovjanske sravnenja / comparanda:** ru: мереологическое слияние; uk: мереологічне злиття; pl: fuzja mereologiczna; cs: mereologická fúze; bcs: mereološka fuzija; мереолошка фузија; bg: мереологична фузия. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[7467]; dictionary_id=35830; lemma=fuzija; gloss=fusion); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** slivanje česti: The native merger phrase is strong for Russian and Ukrainian readers but can describe a process rather than the mereological object or operation and is less uniform across the comparison set. - **Neizvěstnost / uncertainty:** The source does not define overlap or fusion formally.; Mereological fusion is not silently collapsed into the separately displayed least-upper-bound sum in this unit. ## OLISV-T0199 · mereology.improper-part - **English lemma / sense:** improper part — An object considered as a part of itself under reflexive parthood. - **Medžuslovjansky:** `nevlastna čest`; lemma `nevlastna čest`; feminine noun phrase. - **Upotrěbljenje / inflection:** The adjective agrees with čest: genitive nevlastnoj česti; plural nevlastne česti. It includes the whole object itself. - **Kirilična forma:** `невластна чест` - **Argumentacija / rationale:** Nevlastna čest forms the regular negative counterpart to the selected proper-part term and matches the source's explicit example of every object being its own improper part. - **Uvěrjenost / status:** 0.71 (medium); `provisional`; revision `OLISV-T0199-r0001`. - **Slovjanske sravnenja / comparanda:** ru: несобственная часть; uk: невласна частина; pl: część niewłaściwa; cs: nevlastní část; bcs: nepravi dio; неправи део; bg: несъщинска част. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[12327,13541]; dictionary_id=1913,22480; lemma=vlastny; gloss=own/proper); ISV-DICT-LIVE-20260825 (wordList[12471]; dictionary_id=1731; lemma=čęsť; gloss=part); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** nestroga čest: The formal negation of strict is intelligible, but it is less idiomatic and could include incomparable parts rather than specifically the whole object itself. - **Neizvěstnost / uncertainty:** No exact nevlastny dictionary row was found; the term is a transparent project derivation from the selected proper-part family. ## OLISV-T0200 · mereology.mereological-sum - **English lemma / sense:** mereological sum — The displayed least upper bound of two objects under parthood: an object containing both as parts and minimal with that property. - **Medžuslovjansky:** `mereologična suma`; lemma `mereologična suma`; feminine noun phrase. - **Upotrěbljenje / inflection:** The adjective agrees with suma: genitive mereologičnoj sumy; plural mereologične sumy. - **Kirilična forma:** `мереологична сума` - **Argumentacija / rationale:** The international compound is transparent and preserves the displayed order-theoretic definition. It is kept distinct from the later informal fusion term because the source does not define fusion or prove equivalence there. - **Uvěrjenost / status:** 0.89 (high); `provisional`; revision `OLISV-T0200-r0001`. - **Slovjanske sravnenja / comparanda:** ru: мереологическая сумма; uk: мереологічна сума; pl: suma mereologiczna; cs: mereologický součet; bcs: mereološka suma; мереолошка сума; bg: мереологична сума. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[16586]; dictionary_id=1427; lemma=suma; gloss=sum); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** suma česti: The native complement is transparent but can suggest an arithmetic total of parts; the mereological adjective marks the technical order-theoretic operation more reliably. - **Neizvěstnost / uncertainty:** The source's later word fusion is informal and undefined; no equivalence with the displayed sum is assumed in the canon. ## OLISV-T0195 · mereology.mereology - **English lemma / sense:** mereology — The formal and metaphysical study of parts, wholes, parthood, overlap, sums, and fusion. - **Medžuslovjansky:** `mereologija`; lemma `mereologija`; feminine noun. - **Upotrěbljenje / inflection:** Feminine noun; genitive mereologije. Derive the adjective mereologičny, feminine mereologična. - **Kirilična forma:** `мереологија` - **Argumentacija / rationale:** Mereologija is the uniform international name across the six specialist traditions. The source immediately grounds it in the directly frozen concepts of part and relation, preventing the label from remaining opaque. - **Uvěrjenost / status:** 0.84 (high); `provisional`; revision `OLISV-T0195-r0001`. - **Slovjanske sravnenja / comparanda:** ru: мереология; uk: мереологія; pl: mereologia; cs: mereologie; bcs: mereologija; мереологија; bg: мереология. - **Dokazy / evidence:** ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** teorija česti: The descriptive phrase is transparent but names one theory or family of theories rather than the broader discipline and metaphysical subject area. - **Neizvěstnost / uncertainty:** No exact mereologija row occurs in the frozen dictionary response; the selection is an edition-level internationalism. ## OLISV-T0196 · mereology.parthood - **English lemma / sense:** parthood — The relation holding when one object is a part of another; in the displayed basic theory it is axiomatized as a partial order. - **Medžuslovjansky:** `odnošenje česti`; lemma `odnošenje česti`; neuter noun phrase with genitive. - **Upotrěbljenje / inflection:** Neuter head; genitive odnošenja česti. In prose use x jest čestju y for x is part of y. - **Kirilična forma:** `одношење чести` - **Argumentacija / rationale:** The compound uses two direct heads and makes the abstract English suffix transparent. It also provides a stable base for parthood structure, proper part, and improper part. - **Uvěrjenost / status:** 0.76 (medium); `provisional`; revision `OLISV-T0196-r0001`. - **Slovjanske sravnenja / comparanda:** ru: отношение части; uk: відношення частини; pl: relacja bycia częścią; cs: vztah části; bcs: odnos dijela; однос дела; bg: отношение на част. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[14174]; dictionary_id=1992; lemma=odnošeńje; gloss=relation); ISV-DICT-LIVE-20260825 (wordList[12471]; dictionary_id=1731; lemma=čęsť; gloss=part); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** čestnost: A compact abstract derivative would collide with the established honor/honesty family and would be opaque or misleading to many Slavic readers. - **Neizvěstnost / uncertainty:** The frozen part row is marked weaker for several East and South Slavic columns; del/dio/частина remain important comparanda. ## OLISV-T0197 · mereology.parthood-structure - **English lemma / sense:** parthood structure — A first-order structure whose distinguished binary predicate is intended to represent parthood. - **Medžuslovjansky:** `struktura česti`; lemma `struktura česti`; feminine noun phrase with genitive. - **Upotrěbljenje / inflection:** Feminine head; genitive struktury česti, plural struktury česti. The phrase denotes an intended interpretation, not every binary-relation structure. - **Kirilična forma:** `структура чести` - **Argumentacija / rationale:** Struktura česti is compact and compositionally transparent in context. The usage note preserves the source's warning that the label depends on the intended interpretation of the predicate. - **Uvěrjenost / status:** 0.75 (medium); `provisional`; revision `OLISV-T0197-r0001`. - **Slovjanske sravnenja / comparanda:** ru: структура отношения части; uk: структура відношення частини; pl: struktura relacji części; cs: struktura vztahu části; bcs: struktura odnosa dijela; структура односа дела; bg: структура на отношението част. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[16426]; dictionary_id=16363; lemma=struktura; gloss=structure); ISV-DICT-LIVE-20260825 (wordList[12471]; dictionary_id=1731; lemma=čęsť; gloss=part); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** struktura odnošenja česti: The fully explicit compound is precise but heavy in repeated prose; the shorter canonical term remains tied to parthood through its definition and canon link. - **Neizvěstnost / uncertainty:** No exact parthood-structure phrase occurs in the frozen dictionary, and national languages often retain the relation noun explicitly. ## OLISV-T0198 · mereology.proper-part - **English lemma / sense:** proper part — A part of an object that is not identical with the whole object. - **Medžuslovjansky:** `vlastna čest`; lemma `vlastna čest`; feminine noun phrase. - **Upotrěbljenje / inflection:** The adjective agrees with čest: genitive vlastnoj česti; plural vlastne česti. It is the strict, non-reflexive portion of parthood. - **Kirilična forma:** `властна чест` - **Argumentacija / rationale:** Vlastna čest aligns strongly with Ukrainian, Polish, Czech, and Slovak proper-part traditions and remains reconstructible through own/proper senses elsewhere. The source fixes the non-identity boundary. - **Uvěrjenost / status:** 0.72 (medium); `provisional`; revision `OLISV-T0198-r0001`. - **Slovjanske sravnenja / comparanda:** ru: собственная часть; uk: власна частина; pl: część właściwa; cs: vlastní část; bcs: pravi dio; прави део; bg: същинска част. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[12327]; dictionary_id=1913; lemma=vlastny; gloss=own); ISV-DICT-LIVE-20260825 (wordList[13541]; dictionary_id=22480; lemma=vlastny; gloss=proper); ISV-DICT-LIVE-20260825 (wordList[12471]; dictionary_id=1731; lemma=čęsť; gloss=part); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** stroga čest: The strict-order calque is formally transparent but less idiomatic across the comparison traditions and risks suggesting severity rather than non-identity outside formal context. - **Neizvěstnost / uncertainty:** The frozen proper adjective row primarily means suitable or appropriate, so the technical non-identity sense depends on the formal source definition. ## OLISV-T0283 · method.constructive-reasoning - **English lemma / sense:** constructive reasoning — Reasoning that establishes existence or disjunction by supplying the relevant witness, branch, or proof procedure. - **Medžuslovjansky:** `konstruktivno razsuđanje`; lemma `konstruktivno razsuđanje`; neuter adjective verbal-noun phrase. - **Upotrěbljenje / inflection:** Neuter razsuđanje; genitive konstruktivnogo razsuđanja. - **Kirilična forma:** `конструктивно разсуджање` - **Argumentacija / rationale:** The phrase makes the source's proof-giving discipline explicit and reuses the edition's normalized razsuđanje family rather than an ambiguous psychology-oriented thinking term. - **Uvěrjenost / status:** 0.88 (high); `provisional`; revision `OLISV-T0283-r0001`. - **Slovjanske sravnenja / comparanda:** ru: конструктивное рассуждение; uk: конструктивне міркування; pl: rozumowanie konstruktywne; cs: konstruktivní usuzování; bcs: konstruktivno rasuđivanje; конструктивно расуђивање; bg: конструктивно разсъждение. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 13-17 and 74-95); ISV-DICT-LIVE-20260825 (dictionary_id=4873; lemma=konstrukcija; gloss=construction); ISV-DICT-LIVE-20260825 (dictionary_id=34021; lemma=råzsųđati; gloss=pass judgment, reason); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** konstruktivno mysljenje: Mysljenje can denote general thought; the source requires a disciplined inferential practice. - **Neizvěstnost / uncertainty:** The dictionary's råzsųđati spelling is normalized in the edition, and the nominal derivative is compositional rather than directly listed. ## OLISV-T0299 · method.counterexample - **English lemma / sense:** counterexample — An example structure showing that a proposed formula or claim is not valid. - **Medžuslovjansky:** `protivpriměr`; lemma `protivpriměr`; masculine compound noun. - **Upotrěbljenje / inflection:** Masculine protivpriměr; plural protivpriměry, genitive protivpriměra. - **Kirilična forma:** `противпримєр` - **Argumentacija / rationale:** Protivpriměr transparently composes the direct against/example components and states the function of the requested Kripke structure for readers unfamiliar with an international contra- form. - **Uvěrjenost / status:** 0.92 (high); `provisional`; revision `OLISV-T0299-r0001`. - **Slovjanske sravnenja / comparanda:** ru: контрпример; uk: контрприклад; pl: kontrprzykład; cs: protipříklad; bcs: kontraprimjer; контрапример; bg: контрапример. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 220-222); ISV-DICT-LIVE-20260825 (dictionary_id=362; lemma=protiv; gloss=against, contra, versus); ISV-DICT-LIVE-20260825 (dictionary_id=3590; lemma=priměr; gloss=example); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** kontrapriměr: Recognizable, but the direct protiv component gives a more internally transparent Interslavic compound. - **Neizvěstnost / uncertainty:** Most national mathematical traditions use a kontra-/kontro- prefix; protiv- is the edition's transparent pan-Slavic choice. ## OLISV-T0338 · model-theory.adaptation - **English lemma / sense:** adaptation — A version of an existing set of notes modified for use as this Open Logic model-theory part. - **Medžuslovjansky:** `adaptacija`; lemma `adaptacija`; feminine noun. - **Upotrěbljenje / inflection:** Genitive singular adaptacije, instrumental adaptacijeju, and nominative plural adaptacije. - **Kirilična forma:** `адаптација` - **Argumentacija / rationale:** The exact dictionary lemma has unanimous international support and cleanly names a derived textual version. - **Uvěrjenost / status:** 0.99 (high); `provisional`; revision `OLISV-T0338-r0001`. - **Slovjanske sravnenja / comparanda:** ru: адаптация; uk: адаптація, пристосовність; pl: adaptacja, przysposobienie; cs: adaptace, přizpůsobení; bcs: adaptacija; адаптација; bg: адаптация. - **Dokazy / evidence:** OL-MODEL-THEORY-PART (lines 11-12); ISV-DICT-LIVE-20260825 (wordList[283]; dictionary_id=24068; lemma=adaptacija; gloss=adaptation); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** prisposobjeńje: This emphasizes adjustment or customization and is less exact and less uniform for a derived textual edition. - **Neizvěstnost / uncertainty:** The entry is bounded to textual adaptation, not biological adaptation or adaptation as a property. ## OLISV-T0356 · model-theory.back-and-forth-property - **English lemma / sense:** back-and-forth property — The extension condition on a nonempty family of partial isomorphisms: every element of either structure can be added on the corresponding domain or range side. - **Medžuslovjansky:** `svojstvo prodolženja naprěd i nazad`; lemma `svojstvo prodolženja naprěd i nazad`; neuter noun phrase with genitive complement. - **Upotrěbljenje / inflection:** Neuter head svojstvo; genitive svojstva. The paired operational labels are Naprěd and Nazad. Prodolženje names extension of a partial map, not temporal continuation. - **Kirilična forma:** `својство продолжења напрєд и назад` - **Argumentacija / rationale:** Svojstvo prodolženja naprěd i nazad makes the formal action explicit: members of the partial-isomorphism family must be extendible on the domain side and on the range side. The directional words are exceptionally transparent across the dictionary's comparison columns. Polish supplies native paired labels, while Russian and Croatian retain English in academic use, so the full phrase is deliberately presented as an evidence-based Interslavic synthesis rather than a claimed pan-Slavic standard. - **Uvěrjenost / status:** 0.78 (medium); `provisional`; revision `OLISV-T0356-r0001`. - **Slovjanske sravnenja / comparanda:** ru: метод back-and-forth; продолжение частичных изоморфизмов; uk: властивість продовження вперед і назад; pl: warunki Tam i Z powrotem; cs: vlastnost rozšíření vpřed a zpět; bcs: uvjeti (forth) i (back); bg: свойство за продължаване напред и назад. - **Dokazy / evidence:** OL-MODEL-PARTIAL-ISOMORPHISM (lines 40-54); ISV-DICT-LIVE-20260825 (dictionary_id=22019 svojstvo; 4385 prodȯlžeńje; 2791 naprěd; 2781 nazad); PL-UW-PARTIAL-ISOMORPHISM-QUANTIFIER-RANK-N-EQUIVALENCE (physical/printed PDF page 2, Definition 4); HR-ZAGREB-PARTIAL-ISOMORPHISM-QUANTIFIER-RANK-N-EQUIVALENCE (physical PDF page 21, printed page 13); RU-HSE-BACK-AND-FORTH-2012 (HTML line 47, Lecture 1); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; Standard Cyrillic) - **Alternativy / alternatives:** svojstvo naprěd i nazad: The shorter calque is readable but omits the decisive operation—extension of a partial isomorphism—and is therefore less informative out of context.; metod back-and-forth: The borrowed English term is attested in Russian and Croatian academic contexts, but it impedes readers who do not know English and hides the operation that the definition performs. - **Neizvěstnost / uncertainty:** No single native specialist phrase converges across the pinned East-, West-, and South-Slavic sources.; Prodolženje is used in its mathematical extension sense; some readers may prefer razširenje. ## OLISV-T0345 · model-theory.basics - **English lemma / sense:** basics of model theory — The introductory chapter that gathers the foundational topics and prerequisites for the model-theory material. - **Medžuslovjansky:** `osnovy teorije modelov`; lemma `osnova`; noun phrase. - **Upotrěbljenje / inflection:** Osnovy is the nominative plural of feminine osnova ‘basis, base’; teorije is genitive singular of teorija, and modelov is genitive plural of model. Use Osnovy teorije modelov as the chapter title. - **Kirilična forma:** `основы теорије моделов` - **Argumentacija / rationale:** Osnova is the directly pinned Interslavic basis/base noun, and its nominative plural osnovy is the natural chapter-heading form for foundational material. Teorije modelov reuses the already accepted model-theory inflection, yielding a transparent title across Slavic readers. - **Uvěrjenost / status:** 0.94 (high); `provisional`; revision `OLISV-T0345-r0001`. - **Slovjanske sravnenja / comparanda:** ru: основа, база; uk: основа, підстава, база; pl: podstawa, baza; cs: základ, základna; bcs: osnova, baza, temelj; bg: основа, база. - **Dokazy / evidence:** OL-MODEL-BASICS (line 8; \olchapter{mod}{bas}{Basics of Model Theory}); ISV-DICT-LIVE-20260825 (wordList[1719]; dictionary_id=2049; lemma=osnova; gloss=basis, base); ISV-DICT-LIVE-20260825 (wordList[1711]; dictionary_id=2831; lemma=osnovny; gloss=basic, fundamental); ISV-GRAMMAR-ADJ (lines 14-18; agreement and nominal inflection); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** bazis teorije modelov: Bazis is intelligible in some Slavic usage but is not the pinned basic-dictionary head for the general basis/base sense and narrows the pan-Slavic root convergence.; fundamenty teorije modelov: Fundamenty foregrounds a physical foundation and is less suitable for an introductory chapter whose contents are conceptual prerequisites and definitions. - **Neizvěstnost / uncertainty:** The title is an editorial chapter-heading choice; future corpus context may distinguish osnovy from more specialized foundational terminology. ## OLISV-T0363 · model-theory.cantor-dense-order-isomorphism-theorem - **English lemma / sense:** Cantor's isomorphism theorem for dense linear orders — The uniqueness up to order isomorphism of countable dense linear orders without endpoints. - **Medžuslovjansky:** `Kantorova teorema o izomorfizmu gųstyh linearnyh poredkov`; lemma `Kantorova teorema o izomorfizmu gųstyh linearnyh poredkov`; feminine proper-name noun phrase. - **Upotrěbljenje / inflection:** Feminine adjective-noun agreement; genitive Kantorovoj teoremy. Keep the descriptive complement because bare Kantorova teorema is already ambiguous with the power-set theorem. - **Kirilična forma:** `Канторова теорема о изоморфизму густых линеарных поредков` - **Argumentacija / rationale:** The descriptive complement disambiguates this theorem from the power-set result already recorded as OLISV-T0217. Kantorova preserves the canon's deterministic K-to-К script policy, while the remainder composes already established izomorfizm, gųsty, linearny, and poredok heads. Polish directly supplies the Cantor attribution; Russian and Croatian independently fix the proposition and its construction. - **Uvěrjenost / status:** 0.89 (high); `provisional`; revision `OLISV-T0363-r0001`. - **Slovjanske sravnenja / comparanda:** ru: теорема Кантора об изоморфизме счётных плотных линейных порядков; uk: теорема Кантора про ізоморфізм зліченних щільних лінійних порядків; pl: twierdzenie Cantora o izomorfizmie przeliczalnych gęstych porządków liniowych; cs: Cantorova věta o izomorfismu spočetných hustých lineárních uspořádání; bcs: Cantorov teorem o izomorfizmu prebrojivih gustih linearnih poredaka; bg: теорема на Кантор за изоморфизма на изброими гъсти линейни наредби. - **Dokazy / evidence:** OL-MODEL-DENSE-LINEAR-ORDER (lines 28-60); PL-PW-DENSE-LINEAR-ORDER-2022 (physical/printed PDF page 23, Zadanie 181 (Cantor)); RU-MI-RAS-DENSE-LINEAR-ORDER-2015 (physical PDF page 12, problem 10); HR-ZAGREB-DENSE-LINEAR-ORDER-2015 (physical PDF pages 52-53, printed pages 48-49); ISV-TRANSLIT-3.4.4 (package/dist/index.browser.min.js; isv-Cyrl) - **Alternativy / alternatives:** Kantorova teorema: The bare eponym is ambiguous with Cantor's power-set theorem and therefore cannot serve as the machine-indexed canonical head for this result.; teorema Cantora o racionalnom poredku: This foregrounds only the canonical Q representative and obscures the uniqueness theorem for every countable dense no-endpoints order. - **Neizvěstnost / uncertainty:** Only the Polish bounded witness explicitly prints Cantor's name beside this exact theorem; the Russian and Croatian witnesses support the theorem substance independently.; The long descriptive head is intentional for disambiguation; shorter prose may use the theorem label only after the referent is locally clear. ## OLISV-T0244 · model-theory.categorical-description - **English lemma / sense:** categorical description — A description whose models are unique up to isomorphism in the intended class. - **Medžuslovjansky:** `kategoričny opis`; lemma `kategoričny opis`; masculine adjective-noun phrase. - **Upotrěbljenje / inflection:** Genitive kategoričnogo opisa; use kategorično opisanije as the deverbal alternative in prose. - **Kirilična forma:** `категоричны опис` - **Argumentacija / rationale:** Both components are direct dictionary entries, and the target uses the phrase in the model-theoretic sense. The definition is made explicit in the canon so the adjective is not read as merely emphatic. - **Uvěrjenost / status:** 0.9 (high); `provisional`; revision `OLISV-T0244-r0002`. - **Slovjanske sravnenja / comparanda:** ru: категорическое описание; uk: категоричний опис; pl: opis kategoryczny; cs: kategorický popis; bcs: kategorički opis; категорички опис; bg: категорично описание. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (dictionary_id=35597; lemma=kategoričny; gloss=categorical); ISV-DICT-LIVE-20260825 (dictionary_id=20000; lemma=opis; gloss=description); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** jednoznačny opis: Uniqueness alone does not state uniqueness up to isomorphism.; opis po kategorijah: Changes the mathematical notion to a description by categories. - **Neizvěstnost / uncertainty:** The short phrase is context-dependent outside model theory; the source locator fixes its formal sense.; The r0001 record remains preserved as adverse provenance for the target/source locator mismatch. ## OLISV-T0354 · model-theory.complete-theory - **English lemma / sense:** complete theory — A theory that decides every sentence of its language: for each sentence, the theory entails that sentence or its negation. - **Medžuslovjansky:** `polna teorija`; lemma `polna teorija`; feminine adjective-noun phrase. - **Upotrěbljenje / inflection:** The adjective polny agrees with teorija: nominative singular polna teorija, genitive singular polnoj teorije. This is theory completeness by sentence-decision, not completeness of a proof calculus. - **Kirilična forma:** `полна теорија` - **Argumentacija / rationale:** Polna teorija keeps the native full/complete family visible across Russian, Polish, Serbian, Ukrainian, Czech, and Bulgarian comparison evidence and remains continuous with the established canon adjective polny under OLISV-T0061. A separate entry is necessary because this property means deciding every sentence, whereas OLISV-T0061 names completeness of a proof system relative to semantic consequence. The Serbian source makes that distinction on adjacent pages, so identical surface morphology does not erase the polysemy boundary. - **Uvěrjenost / status:** 0.94 (high); `provisional`; revision `OLISV-T0354-r0001`. - **Slovjanske sravnenja / comparanda:** ru: полная теория; uk: повна теорія; pl: teoria zupełna; cs: úplná teorie; bcs: kompletna ili potpuna teorija; комплетна или потпуна теорија; bg: пълна теория. - **Dokazy / evidence:** OL-MODEL-THEORY-M (lines 29-53); ISV-DICT-LIVE-20260825 (wordList[3816]; dictionary_id=10923; popȯlny; and wordList[7429]; dictionary_id=3141; pȯlny); RU-MSU-COMPLETE-THEORY-2026 (PDF slides 6-11); PL-AMU-COMPLETE-THEORY-2020 (physical PDF pages 25-26, Theorem 1.11); SR-BELGRADE-COMPLETE-THEORY (physical PDF pages 47-49, printed pages 39-41); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; Standard Cyrillic) - **Alternativy / alternatives:** kompletna teorija: The international adjective is directly attested as a Serbian synonym and is broadly recognizable, but it is less continuous with the established edition family polnota/polny and less transparent to readers relying on the native full/whole cognate family.; teorija, ktora odlučaje vsako izrečenje: This explanatory clause is useful in the definition but too long for the recurring canonical head and would obscure correspondence with the standard Slavic specialist terminology. - **Neizvěstnost / uncertainty:** Polny is an established edition normalization; the pinned dictionary marks the direct adjective as pȯlny or popȯlny.; The Polish and Serbian sources state the criterion deductively, while the Russian and Open Logic sources state it semantically; completeness of first-order logic makes the criteria coincide under their respective theory conventions, but the entry preserves the Open Logic semantic locator as authority. ## OLISV-T0397 · model-theory.computable-model - **English lemma / sense:** computable model — A model presented as a computable arithmetic structure on the natural numbers; in this unit, the term is used for models of Q, PA, and true arithmetic. - **Medžuslovjansky:** `izčislimy model`; lemma `izčislimy model`; masculine adjective-noun phrase. - **Upotrěbljenje / inflection:** Izčislimy agrees with masculine model; nominative plural is izčislimy modeli. The adjective describes the presentation of the structure, not the cardinality of its domain. - **Kirilična forma:** `изчислимы модел` - **Argumentacija / rationale:** The phrase directly combines the active computability and model heads, has a pinned Russian specialist counterpart, and stays visibly distinct from izčisljivy model, the canon's countable-model phrase. - **Uvěrjenost / status:** 0.95 (high); `provisional`; revision `OLISV-T0397-r0001`. - **Slovjanske sravnenja / comparanda:** ru: вычислимая модель; uk: обчислювана модель; pl: model obliczalny; cs: vyčíslitelný model; bcs: izračunljiv model; израчунљив модел; bg: изчислим модел. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[2804]; dictionary_id=5879; active canon=OLISV-T0023-r0001); ISV-DICT-LIVE-20260825 (wordList[11194]; dictionary_id=19859; active canon=OLISV-T0017-r0002); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic and standard flavorization) - **Alternativy / alternatives:** izčisljivy model: Canon T0384 reserves this surface for countable model; using it here would erase the theorem's computability claim.; algoritmičny model: This suggests an algorithmic presentation but is not the canon's established computable adjective and weakens exact term continuity. - **Neizvěstnost / uncertainty:** West- and South-Slavic full phrases are componential comparisons rather than direct pinned specialist quotations. ## OLISV-T0396 · model-theory.computable-structure - **English lemma / sense:** computable structure — An arithmetic structure with domain the natural numbers whose successor, addition, and multiplication interpretations are computable functions and whose order is decidable. - **Medžuslovjansky:** `izčislima struktura`; lemma `izčislima struktura`; feminine adjective-noun phrase. - **Upotrěbljenje / inflection:** Izčislima agrees with feminine struktura. Use izčislimu strukturu in the accusative and izčislime struktury in the nominative plural. - **Kirilična forma:** `изчислима структура` - **Argumentacija / rationale:** The compound composes two already active canon heads without creating a synonym. It preserves the source's exact distinction: the operations are computable, while the order relation is decidable. - **Uvěrjenost / status:** 0.93 (high); `provisional`; revision `OLISV-T0396-r0001`. - **Slovjanske sravnenja / comparanda:** ru: вычислимая структура; uk: обчислювана структура; pl: struktura obliczalna; cs: vyčíslitelná struktura; bcs: izračunljiva struktura; израчунљива структура; bg: изчислима структура. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[2804]; dictionary_id=5879; active canon=OLISV-T0023-r0001); ISV-DICT-LIVE-20260825 (wordList[16426]; dictionary_id=16363; active canon=OLISV-T0016-r0001); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic and standard flavorization) - **Alternativy / alternatives:** izčisljiva struktura: The -ljiv- form is reserved by canon T0066/T0067 for countability or enumerability and would collapse two different properties.; kompjutabilna struktura: The internationalism is less transparent than the accepted izčisl- family and breaks continuity with canon T0023. - **Neizvěstnost / uncertainty:** The full compound is an edition-level composition; the frozen official dictionary does not list the specialist phrase as one headword. ## OLISV-T0384 · model-theory.countable-model - **English lemma / sense:** countable or enumerable model — A model whose domain is finite or countably infinite under the edition's inclusive enumerable convention; the OLP-0194 compactness theory forces the present model to be infinite. - **Medžuslovjansky:** `izčisljivy model`; lemma `izčisljivy model`; masculine adjective-noun phrase. - **Upotrěbljenje / inflection:** Masculine singular izčisljivy model. The adjective describes the domain's cardinality, not effective computability; use izčisljivo bezkonečny only when countable infinitude is foregrounded. - **Kirilična forma:** `изчисљивы модел` - **Argumentacija / rationale:** Izčisljivy model composes the established inclusive countability adjective with model. The use note explicitly blocks confusion with izčislimy, which denotes computability, and records why finite inclusion is harmless although the current construction is necessarily infinite. - **Uvěrjenost / status:** 0.7 (medium); `provisional`; revision `OLISV-T0384-r0001`. - **Slovjanske sravnenja / comparanda:** ru: счётная модель; uk: зліченна модель; pl: przeliczalny model; cs: spočetný model; bcs: prebrojiv model; bg: изброим модел. - **Dokazy / evidence:** OL-MODEL-ARITHMETIC-NONSTANDARD-MODELS (lines 79-113 plus localized proof completion); OL-COM-DOWNWARD-LS (lines 13-23); ISV-DICT-LIVE-20260825 (wordList[2804]; dictionary_id=5879; lemma=izčisliti); PL-UW-MATHEMATICAL-LOGIC-2014-15 (printed page 27 / extracted lines 1358-1367); UK-KNU-MODEL-THEORY-2023 (decoded lines 1944-2008); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic, standard flavorization) - **Alternativy / alternatives:** izčislimy model: This suggests a computable presentation or decision procedure rather than countable cardinality.; izčisljivo bezkonečny model: Extensionally correct here but stronger in surface wording than the source's inclusive enumerable term. - **Neizvěstnost / uncertainty:** The specialist cardinality adjective is derived from the established canon term rather than directly listed as such in the official dictionary. ## OLISV-T0166 · model-theory.covered-structure - **English lemma / sense:** covered structure — A structure in which every element of the domain is the semantic value of some closed term. - **Medžuslovjansky:** `pokryta struktura`; lemma `pokryta struktura`; feminine noun phrase. - **Upotrěbljenje / inflection:** The resultative participle agrees with struktura: nominative singular pokryta struktura, masculine model pokryty, and non-masculine plural pokryte struktury. - **Kirilična forma:** `покрыта структура` - **Argumentacija / rationale:** Pokryta struktura preserves the source label and states the defined extensional condition as a completed property. The frozen dictionary provides both aspectual cover verbs and the structure head across East, West, and South Slavic columns; the source supplies the exact model-theoretic sense and agreement contexts. - **Uvěrjenost / status:** 0.82 (high); `provisional`; revision `OLISV-T0166-r0001`. - **Slovjanske sravnenja / comparanda:** ru: покрытая структура; uk: покрита структура; pl: struktura pokryta; cs: pokrytá struktura; bcs: pokrivena struktura; покривена структура; bg: покрита структура. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-DICT-LIVE-20260825 (wordList[4342], wordList[4343], wordList[16426]; dictionary_id=158,1769,16363); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** struktura pokryta značenjami zamknutyh termov: Semantically exact as an explanatory definition but too long and syntactically marked for the stable headword.; struktura generovana zamknutymi termami: Changes the source label and risks conflation with generated-substructure terminology.; pokryvana struktura: The imperfective participle suggests an ongoing process rather than the defined extensional state. - **Neizvěstnost / uncertainty:** The complete specialist phrase and resultative participle are editorial formations rather than direct frozen-dictionary headwords.; The English notion is signature-dependent: coverage is determined by which constants and functions generate closed terms. ## OLISV-T0181 · model-theory.definability - **English lemma / sense:** definability — The possibility of defining one concept or relation in terms of other primitives of a theory, so it need not receive a separate interpretation in each model. - **Medžuslovjansky:** `definovateljnost`; lemma `definovateljnost`; feminine abstract noun. - **Upotrěbljenje / inflection:** Decline as a feminine consonant noun: genitive definovateljnosti. The corresponding adjective is definovateljny. - **Kirilična forma:** `дефиноватељност` - **Argumentacija / rationale:** Definovateljnost keeps the directly attested defin- international root and selects a -telj- ability formation that is transparent in Polish, Czech, Slovak, and South Slavic traditions. The source explanation ties the noun to elimination of a separately interpreted primitive, making the specialist sense explicit. - **Uvěrjenost / status:** 0.71 (medium); `provisional`; revision `OLISV-T0181-r0001`. - **Slovjanske sravnenja / comparanda:** ru: определимость; uk: визначуваність; pl: definiowalność; cs: definovatelnost; bcs: definabilnost; odredljivost; bg: определимост. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[4855,4862]; dictionary_id=4956,2624; lemma=definiovati,definicija; gloss=define,definition); ISV-DICT-LIVE-20260825 (wordList[5319]; dictionary_id=36455; lemma=råzpoznavajemosť; gloss=discernibility, recognizability); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** definovajemosť: The -jemosť pattern is productive and more directly analogous to a frozen dictionary row, but definovateljnost better bridges Polish definiowalność, Czech/Slovak definovatelnost, and South Slavic -ljiv/-abil- traditions while remaining transparent to East Slavic readers. - **Neizvěstnost / uncertainty:** No frozen Interslavic dictionary row directly attests definovateljnost.; The selected derivation is an editorial pan-Slavic compromise among several productive national formations. ## OLISV-T0361 · model-theory.dense-linear-order-without-endpoints - **English lemma / sense:** dense linear order without endpoints — A strict dense linear order having neither a least element nor a greatest element. - **Medžuslovjansky:** `gųsty linearny poredok bez krajnyh elementov`; lemma `gųsty linearny poredok bez krajnyh elementov`; masculine noun phrase with prepositional modifier. - **Upotrěbljenje / inflection:** Plural gųste linearne poredky bez krajnyh elementov. At first definition, gloss bez krajnyh elementov explicitly as bez najmenšego i največšego elementa. - **Kirilična forma:** `густы линеарны поредок без крајных елементов` - **Argumentacija / rationale:** The compact phrase keeps the Open Logic technical label while the mandatory first-use gloss states the exact least/greatest semantics for readers who do not know the English term. Gųsty is directly supported by the official dictionary and West/South Slavic witnesses; linearny poredok reuses OLISV-T0038; krajny is an official dictionary component whose potentially broader everyday sense is controlled by the explicit gloss and six axioms. - **Uvěrjenost / status:** 0.9 (high); `provisional`; revision `OLISV-T0361-r0001`. - **Slovjanske sravnenja / comparanda:** ru: плотный линейный порядок без концевых точек; uk: щільний лінійний порядок без найменшого і найбільшого елемента; pl: gęsty porządek liniowy bez elementu największego i najmniejszego; cs: husté lineární uspořádání bez nejmenšího a největšího prvku; bcs: gust linearno uređen skup bez najmanjeg i najvećeg elementa; bg: гъста линейна наредба без най-малък и най-голям елемент. - **Dokazy / evidence:** OL-MODEL-DENSE-LINEAR-ORDER (lines 10-26); ISV-DICT-LIVE-20260825 (dictionary_id=5308 gųsty; dictionary_id=757 krajny); RU-MI-RAS-DENSE-LINEAR-ORDER-2015 (physical PDF page 12, problem 10); PL-PW-DENSE-LINEAR-ORDER-2022 (physical/printed PDF page 23, Zadanie 181); HR-ZAGREB-DENSE-LINEAR-ORDER-2015 (physical PDF page 52, printed page 48, Theorem 1.77); ISV-TRANSLIT-3.4.4 (package/dist/index.browser.min.js; isv-Cyrl) - **Alternativy / alternatives:** gųsty linearny poredok bez koncov: The short calque is superficially close to Russian but can be read as temporal or physical ends and does not identify the least/greatest order elements for a general reader.; gųsty linearny poredok bez granic: Boundary language is not the order-theoretic concept and risks suggesting boundedness in a metric or topological sense. - **Neizvěstnost / uncertainty:** Krajny is broader in ordinary language than the specialist endpoint sense, so the explicit first-use gloss remains part of the house policy.; No official Interslavic specialist dictionary entry for the entire phrase was found in the bounded evidence set. ## OLISV-T0081 · model-theory.discipline - **English lemma / sense:** model theory — The branch of logic studying formal structures, their theories, and sentences characterizing classes of structures. - **Medžuslovjansky:** `teorija modelov`; lemma `teorija modelov`; feminine noun phrase. - **Upotrěbljenje / inflection:** Use v teoriji modelov and genitive plural modelov throughout the edition. - **Kirilična forma:** `теорија моделов` - **Argumentacija / rationale:** The genitive construction mirrors the overwhelmingly convergent Slavic specialist phrase and preserves the existing model and teorija lemmas. - **Uvěrjenost / status:** 0.94 (high); `provisional`; revision `OLISV-T0081-r0001`. - **Slovjanske sravnenja / comparanda:** ru: теория моделей; uk: теорія моделей; pl: teoria modeli; cs: teorie modelů; bcs: teorija modela; bg: теория на моделите. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[11194], wordList[17168]; dictionary_id=19859,4739); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** modelna teorija: The adjective is readable but less aligned with the dominant national genitive construction. - **Neizvěstnost / uncertainty:** The complete phrase is compositionally established rather than directly listed. ## OLISV-T0236 · model-theory.disjoint-domains - **English lemma / sense:** disjoint domains — The carrier domains of distinct sorts have empty pairwise intersections. - **Medžuslovjansky:** `vzajemno neprěsěčne domeny`; lemma `vzajemno neprěsěčne domeny`; plural adjective-noun phrase. - **Upotrěbljenje / inflection:** Genitive vzajemno neprěsěčnyh domenov; use the singular explanatory clause domeny ne prěsěkaju se. - **Kirilična forma:** `взајемно непрєсєчне домены` - **Argumentacija / rationale:** The selected phrase states the required empty-intersection condition instead of weakening it to mere separateness. - **Uvěrjenost / status:** 0.78 (high); `provisional`; revision `OLISV-T0236-r0001`. - **Slovjanske sravnenja / comparanda:** ru: попарно непересекающиеся домены; uk: попарно неперетинні домени; pl: parami rozłączne dziedziny; cs: po dvou disjunktní domény; bcs: uzajamno disjunktne domene; узајамно дисјунктни домени; bg: взаимно непресичащи се домейни. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[15106]; dictionary_id=3990; lemma=odděľny; gloss=separate); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** odděľne domeny: Separate does not by itself guarantee empty intersections.; disjunktne domeny: Precise but less accessible in public-facing prose than the transparent intersection family. - **Neizvěstnost / uncertainty:** The selected complete phrase is compositionally derived; the direct dictionary row supports only the weaker adverse alternative. ## OLISV-T0084 · model-theory.domain - **English lemma / sense:** domain of a structure — The underlying set of objects over which a first-order structure interprets its language; in a many-sorted structure, also the carrier assigned to one sort before the carriers are combined in the first-order encoding. - **Medžuslovjansky:** `domen struktury`; lemma `domen struktury`; masculine noun phrase. - **Upotrěbljenje / inflection:** Genitive singular domena struktury. Bare domen is allowed when context fixes the structure; use domen sorta for one sort's carrier. Do not conflate this with domen funkcije. - **Kirilična forma:** `домен структуры` - **Argumentacija / rationale:** The established domain head remains stable. OLP-0176 adds a controlled many-sorted extension: each sort has a carrier domain, while the embedding combines those carriers into one first-order domain. - **Uvěrjenost / status:** 0.85 (high); `provisional`; revision `OLISV-T0084-r0002`. - **Slovjanske sravnenja / comparanda:** ru: домен структуры; uk: домен структури; pl: dziedzina struktury; domena struktury; cs: doména struktury; univerzum struktury; bcs: domena strukture; bg: домейн на структурата. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[5559]; dictionary_id=36356); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** univerzum struktury: Common in some traditions but can suggest a broader set-theoretic universe.; oblast struktury: Ordinary spatial and administrative readings are less precise than the direct headword. - **Neizvěstnost / uncertainty:** National accounts also use universe/carrier terminology; domen remains the edition head. ## OLISV-T0390 · model-theory.element-block - **English lemma / sense:** block of an element — The equivalence class of an element of a PA-model under finite standard successor distance; non-standard blocks have order type of the integers. - **Medžuslovjansky:** `blok elementa`; lemma `blok elementa`; masculine noun phrase. - **Upotrěbljenje / inflection:** Blok is masculine; the defining element is genitive singular elementa. Use standardny blok and nestandardny blok for the two scoped variants. - **Kirilična forma:** `блок елемента` - **Argumentacija / rationale:** The transparent genitive compound follows the source's own block notation, uses two directly attested pan-Slavic components, and leaves the finite-distance definition explicit instead of loading extra meaning into blok. - **Uvěrjenost / status:** 0.88 (high); `provisional`; revision `OLISV-T0390-r0001`. - **Slovjanske sravnenja / comparanda:** ru: блок элемента; uk: блок елемента; pl: blok elementu; cs: blok prvku; bcs: blok elementa; блок елемента; bg: блок на елемента. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[2218]; dictionary_id=2459; lemma=blok; gloss=bloc); ISV-DICT-LIVE-20260825 (wordList[6006]; dictionary_id=17372; lemma=element; gloss=element); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic and standard flavorization) - **Alternativy / alternatives:** klasa elementa: Klasa hides the source's deliberate block metaphor and can be confused with the full equivalence-class construction.; cělosť elementa: The whole or entirety reading is not the named quotient component and lacks the direct cross-Slavic block convergence. - **Neizvěstnost / uncertainty:** The frozen dictionary attests everyday bloc rather than the full specialist equivalence-class compound. ## OLISV-T0351 · model-theory.elementary-equivalence - **English lemma / sense:** elementary equivalence — The relation between first-order structures that satisfy exactly the same sentences in the common language. - **Medžuslovjansky:** `elementarna ekvivalentnost`; lemma `elementarna ekvivalentnost`; feminine abstract noun phrase. - **Upotrěbljenje / inflection:** Use elementarna ekvivalentnost for the relation. In predicative and attributive use, inflect elementarno ekvivalentny for the gender, number, and case of the structures being compared. - **Kirilična forma:** `елементарна еквивалентност` - **Argumentacija / rationale:** Elementarna ekvivalentnost preserves the international elementary-equivalence term family while using two independently published Interslavic components. Direct Ukrainian, Czech, Polish, Montenegrin, and Croatian academic evidence shows that the same transparent family is recognizable across East, West, and South Slavic model theory. The adjective in the translated definition is inflected to agree with struktura, while the canon head remains the abstract name of the relation. - **Uvěrjenost / status:** 0.96 (high); `provisional`; revision `OLISV-T0351-r0001`. - **Slovjanske sravnenja / comparanda:** ru: элементарная эквивалентность; uk: елементарна еквівалентність; pl: równoważność elementarna; cs: elementární ekvivalence; bcs: elementarna ekvivalencija; елементарна еквиваленција; bg: елементарна еквивалентност. - **Dokazy / evidence:** OL-MODEL-ISOMORPHISM (lines 12-34 and 62-66); ISV-DICT-LIVE-20260825 (wordList[6009], wordList[6276]; dictionary_id=35208,36133; elementarny and ekvivalentny); UK-KNU-ISOMORPHISM-AUTOMORPHISM-ELEMENTARY-EQUIVALENCE-2022 (physical/printed PDF page 127, section 4.4); CS-CUNI-ISOMORPHISM-ELEMENTARY-EQUIVALENCE (physical PDF pages 24-25, printed pages 96-98); PL-UW-ISOMORPHISM-AUTOMORPHISM (physical PDF pages 15-18); ME-UCG-MODEL-ISOMORPHISM (physical PDF pages 84-85); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; Standard Cyrillic) - **Alternativy / alternatives:** elementarna ravnovrednost: Ravnovrednost is broadly intelligible but can suggest equal value rather than equivalence with respect to all first-order sentences, and it weakens continuity with the attested specialist ekvivalent- family.; logična ekvivalentnost struktur: This risks confusion with logical equivalence of formulas; elementary equivalence is specifically a relation between structures satisfying the same first-order sentences. - **Neizvěstnost / uncertainty:** The official Interslavic dictionary pins the two components separately, not the complete model-theory phrase.; The Ukrainian textbook phrases its definition over formulas; the Open Logic locator remains authority for the edition's sentence-only formulation. ## OLISV-T0385 · model-theory.elementary-substructure - **English lemma / sense:** elementary substructure — A substructure that agrees with the ambient structure on the truth of every first-order formula with parameters from the substructure; used here to preserve the expanded theory and named constant while reducing cardinality. - **Medžuslovjansky:** `elementarna podstruktura`; lemma `elementarna podstruktura`; feminine adjective-noun phrase. - **Upotrěbljenje / inflection:** Feminine singular elementarna podstruktura; genitive elementarnoj podstruktury. Do not weaken it to an arbitrary podstruktura, which need not preserve all formulas. - **Kirilična forma:** `елементарна подструктура` - **Argumentacija / rationale:** Elementarna podstruktura is nearly identical to the directly attested Polish phrase and transparently combines an official adjective with the established podstruktura canon entry. It names the preservation strength actually required by the proof, not merely domain inclusion. - **Uvěrjenost / status:** 0.91 (high); `provisional`; revision `OLISV-T0385-r0001`. - **Slovjanske sravnenja / comparanda:** ru: элементарная подструктура; uk: елементарна підсистема; pl: elementarna podstruktura; cs: elementární podstruktura; bcs: elementarna podstruktura; bg: елементарна подструктура. - **Dokazy / evidence:** OL-COM-DOWNWARD-LS (lines 13-23); ISV-DICT-LIVE-20260825 (wordList[6009]; dictionary_id=35208; lemma=elementarny); ISV-DICT-LIVE-20260825 (wordList[16426,17919]; dictionary_id=16363,737; struktura and pod); PL-UW-MATHEMATICAL-LOGIC-2014-15 (printed page 24 / extracted lines 1191-1200); UK-KNU-MODEL-THEORY-2023 (decoded lines 5000-5029); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic, standard flavorization) - **Alternativy / alternatives:** podstruktura: An arbitrary substructure need not preserve the truth of every formula and therefore does not close the proof gap.; elementarna podsistema: Ukrainian directly uses the system head, but podstruktura aligns with the existing edition canon and Polish/Czech/Serbian model-theory terminology. - **Neizvěstnost / uncertainty:** Russian, Czech, BCS, and Bulgarian complete phrases are editorial in this packet rather than direct printed attestations. ## OLISV-T0343 · model-theory.exercise - **English lemma / sense:** exercise — A pedagogical problem or assigned task through which a textbook reader practices the model-theory material. - **Medžuslovjansky:** `zadanje`; lemma `zadańje`; neuter noun. - **Upotrěbljenje / inflection:** Genitive singular and nominative plural zadańja. The dictionary head preserves its marked notation; the preferred running surface is normalized zadanje/zadanja for deterministic standard-flavor projection. - **Kirilična forma:** `задање` - **Argumentacija / rationale:** The exact pinned exercise sense belongs to the most broadly shared Slavic task/problem family. The marked dictionary lemma remains the lexical witness, while the preferred running surface is normalized so the official Cyrillic replay is exact. - **Uvěrjenost / status:** 0.91 (high); `provisional`; revision `OLISV-T0343-r0001`. - **Slovjanske sravnenja / comparanda:** ru: задание, задача; uk: завдання, задача; pl: zadanie; cs: zadání, úkol, úloha, cvičení; bcs: zadatak, zadaća; задатак, задаћа; bg: задание, задача. - **Dokazy / evidence:** OL-MODEL-THEORY-PART (lines 14-15); ISV-DICT-LIVE-20260825 (wordList[16944]; dictionary_id=3958; lemma=zadańje; gloss=task, assignment, exercise); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** upražnjenje: This plausible exercise form is not the pinned basic-dictionary head and is liable to physical-practice ambiguity. - **Neizvěstnost / uncertainty:** Context must distinguish a pedagogical exercise from a general operational task. ## OLISV-T0372 · model-theory.existential-witness - **English lemma / sense:** existential witness — An element making an existential formula true in a structure; here it internally satisfies the proof-code predicate but need not be an actual standard derivation. - **Medžuslovjansky:** `svědok`; lemma `svědok`; masculine animate noun. - **Upotrěbljenje / inflection:** Masculine animate noun: svědok; genitive/accusative svědka; plural svědky. The mathematical role is fixed by the existential formula, not by the ordinary legal sense. - **Kirilična forma:** `свєдок` - **Argumentacija / rationale:** Svědok normalizes the direct dictionary lemma svědȯk to the edition's standard surface and gains specialist precision from the explicit existential formula. Ukrainian and Polish academic witnesses independently show that the ordinary witness family extends naturally into model theory. The element is a semantic witness inside the non-standard model; it is not thereby an actual standard proof. - **Uvěrjenost / status:** 0.87 (high); `provisional`; revision `OLISV-T0372-r0001`. - **Slovjanske sravnenja / comparanda:** ru: свидетель; uk: свідок; pl: świadek; cs: svědek; bcs: svjedok; сведок; bg: свидетел. - **Dokazy / evidence:** OL-MODEL-ARITHMETIC-INTRODUCTION (lines 64-71); ISV-DICT-LIVE-20260825 (wordList[18895]; dictionary_id=21168; lemma=svědȯk; gloss=witness); UK-KNU-LOGIC-FOUNDATIONS-2020 (physical page 88 / extracted lines 3758-3780); PL-UW-MATHEMATICAL-LOGIC-2014-15 (extracted line 1475); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic, standard flavorization) - **Alternativy / alternatives:** dokaz: A proof or piece of evidence is not the object instantiating an existential quantifier; using dokaz would collapse witness and derivation.; svěditelj: This East- and Bulgarian-facing form is recognizable but is less balanced than the direct Interslavic dictionary lemma and the Ukrainian/Polish/Czech witness family. - **Neizvěstnost / uncertainty:** The dictionary lemma is general-purpose; the mathematical sense is an edition-level specialization fixed by the formula and academic comparanda.; The exact normalized surface svědok differs from the etymological-vowel dictionary spelling svědȯk. ## OLISV-T0347 · model-theory.expansion - **English lemma / sense:** expansion — A structure for a larger language that keeps the same domain and the same interpretations of every symbol from the smaller language while adding interpretations for the additional symbols. - **Medžuslovjansky:** `razširjenje`; lemma `råzširjeńje`; neuter noun. - **Upotrěbljenje / inflection:** The dictionary preserves etymological råzširjeńje; running standard-flavor prose uses razširjenje, genitive razširjenja, instrumental razširjenjem, and nominative plural razširjenja. - **Kirilična forma:** `разширјење` - **Argumentacija / rationale:** Razširjenje is the direct Interslavic dictionary head for extension and expansion after standard-flavor normalization. Its root is transparent across East, West, and South Slavic comparanda, it already appears consistently in the accepted Henkin-expansion material, and the Serbian model-theory witness uses the cognate proširenje for language expansion. It therefore gives broader practical comprehension than the competing internationalism ekspansija while preserving the exact Open Logic sense. - **Uvěrjenost / status:** 0.98 (high); `provisional`; revision `OLISV-T0347-r0001`. - **Slovjanske sravnenja / comparanda:** ru: расширение; uk: розширення; pl: rozszerzenie, poszerzenie; cs: rozšíření; expanze; bcs: proširenje, proširivanje, širenje; проширење, раширење; bg: разширение. - **Dokazy / evidence:** OL-MODEL-REDUCTS-EXPANSIONS (lines 12-39 and 59-65); ISV-DICT-LIVE-20260825 (wordList[6582]; dictionary_id=3601; lemma=råzširjeńje; gloss=extension, expansion, extension, widening); OL-COM-HENKIN-ISV (lines 11, 18, 74-75, and 80-82); CS-VPL-REDUCT-EXPANSION (physical PDF page 71, printed slides 35-40); SR-KG-REDUCT-EXPANSION-2013 (physical PDF page 74, printed page 69: L* proširenje jezika L); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** ekspansija: The dictionary directly attests this international alternative, and Czech specialist usage supports it, but the native razšir- family has broader cross-Slavic convergence and already governs the accepted edition's logical expansion prose.; proširjenje: This South-Slavic-weighted prefix is directly understandable and domain-attested, but razširjenje better aligns the broader East/West/South dictionary convergence and the edition's existing canonical surface. - **Neizvěstnost / uncertainty:** The dictionary head covers extension, expansion, and widening; the Open Logic locator supplies the specialist model-theory sense boundary.; Czech technical usage favors the competing international expanze, while South-Slavic usage prefers proširenje; the selected razširjenje is an editorial pan-Slavic compromise. ## OLISV-T0337 · model-theory.experimental-material - **English lemma / sense:** experimental — Presented provisionally as material still being tried and developed, rather than as a mature finished textbook treatment. - **Medžuslovjansky:** `eksperimentaľny`; lemma `eksperimentaľny`; adjective. - **Upotrěbljenje / inflection:** Agree regularly with the head noun. The canonical dictionary head is eksperimentaľny; running standard-flavor prose uses normalized eksperimentalny/eksperimentalne surfaces. - **Kirilična forma:** `експерименталны` - **Argumentacija / rationale:** The exact international head is directly attested and supplies the strongest six-tradition convergence. - **Uvěrjenost / status:** 0.97 (high); `provisional`; revision `OLISV-T0337-r0001`. - **Slovjanske sravnenja / comparanda:** ru: экспериментальный; uk: експериментальний; pl: eksperymentalny; cs: experimentální, pokusný; bcs: eksperimentalan, pokusni; експерименталан, огледан; bg: опитен, експериментален. - **Dokazy / evidence:** OL-MODEL-THEORY-PART (lines 10-11); ISV-DICT-LIVE-20260825 (wordList[6523]; dictionary_id=20374; lemma=eksperimentaľny; gloss=experimental); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** pokusny: The West-oriented trial adjective is less uniform and may denote a test specimen rather than developmental editorial status. - **Neizvěstnost / uncertainty:** This is an editorial-development status, not experimental logic or an empirical experiment. ## OLISV-T0342 · model-theory.explanation - **English lemma / sense:** explanation — Expository material that makes the model-theory content and its reasoning understandable. - **Medžuslovjansky:** `objasnjenje`; lemma `objasnjeńje`; neuter noun. - **Upotrěbljenje / inflection:** Genitive singular and nominative plural objasnjeńja. The dictionary head remains objasnjeńje; the preferred running surface is normalized objasnjenje/objasnjenja, whose nj sequences are projected deterministically by the pinned official scheme. - **Kirilična forma:** `објасњење` - **Argumentacija / rationale:** The direct explanation head has especially strong South-Slavic identity and clear recognition elsewhere. The marked dictionary lemma is retained for evidence, while the preferred running surface is normalized for the official script projection. - **Uvěrjenost / status:** 0.97 (high); `provisional`; revision `OLISV-T0342-r0001`. - **Slovjanske sravnenja / comparanda:** ru: объяснение, разъяснение, толкование; uk: пояснення, тлумачення; pl: objaśnienie, wyjaśnienie, tłumaczenie; cs: vysvětlení; bcs: objašnjenje, razjašnjenje, tumačenje; објашњење; bg: обяснение. - **Dokazy / evidence:** OL-MODEL-THEORY-PART (line 14); ISV-DICT-LIVE-20260825 (wordList[6528]; dictionary_id=3608; lemma=objasnjeńje; gloss=explanation); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** tolkovanje: An interpretation/commentary family is narrower than the general explanatory material required here. - **Neizvěstnost / uncertainty:** Keep this general expository sense distinct from formal justification, proof, and causal explanation. ## OLISV-T0349 · model-theory.extension-by-domain - **English lemma / sense:** extension — A structure for the same language whose domain includes that of a substructure and whose interpretations restrict to the substructure interpretations on the smaller domain. - **Medžuslovjansky:** `razširjenje`; lemma `råzširjeńje`; neuter noun. - **Upotrěbljenje / inflection:** Running standard-flavor prose uses razširjenje, genitive razširjenja, instrumental razširjenjem, and nominative plural razširjenja. This entry is sense-distinct from the richer-language expansion recorded by OLISV-T0347. - **Kirilična forma:** `разширјење` - **Argumentacija / rationale:** Razširjenje is already the directly attested Interslavic head for extension and the accepted edition surface for structure expansion. Reusing it here reflects broad East-West-South convergence, while the separate canon key prevents the same-language larger-domain relation from being confused with OLP-0184's richer-language, same-domain expansion. The Polish evidence combines a direct podstruktura definition with the dictionary's cognate rozszerzenie family; the Serbian source exposes ekstenzija as a real same-neighborhood specialist alternative, but the native family remains more broadly transparent. - **Uvěrjenost / status:** 0.97 (high); `provisional`; revision `OLISV-T0349-r0001`. - **Slovjanske sravnenja / comparanda:** ru: расширение; uk: розширення; pl: rozszerzenie; cs: rozšíření; bcs: proširenje; ekstenzija; проширење; екстензија; bg: разширение. - **Dokazy / evidence:** OL-MODEL-SUBSTRUCTURES (lines 19-37, especially definition defn:substructure); ISV-DICT-LIVE-20260825 (wordList[6582]; dictionary_id=3601; lemma=råzširjeńje; gloss=extension, expansion, extension, widening); SR-KG-REDUCT-EXPANSION-2013 (physical PDF page 27, printed page 23); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** ekstenzija: The Serbian source directly attests this internationalism for a structural extension, but the native razšir- family is directly present in the Interslavic dictionary and converges more broadly across the comparison languages.; nadstruktura: This would be a transparent reverse compound, but it would create an unnecessary new head where the dictionary already supplies extension and the Open Logic source explicitly labels the reverse relation as extension. - **Neizvěstnost / uncertainty:** The dictionary head is polysemous across extension, expansion, and widening; the canon key and Open Logic locator are therefore required to disambiguate this same-language structural sense.; Serbian exact-domain specialist usage favors ekstenzija, while the selected native family is justified by wider cross-Slavic recognizability. ## OLISV-T0065 · model-theory.factor-structure - **English lemma / sense:** factor structure — A quotient structure whose domain consists of equivalence classes and whose interpretations are induced from the original structure. - **Medžuslovjansky:** `faktorna struktura`; lemma `faktorna struktura`; feminine noun phrase. - **Upotrěbljenje / inflection:** The feminine adjective faktorna agrees with struktura; use faktornej struktury in the genitive singular. - **Kirilična forma:** `факторна структура` - **Argumentacija / rationale:** Faktorna struktura follows Open Logic's factor construction, combines the directly supported structure lemma with an inherited factor adjective used in the quotient sense, and keeps Polish and BCS quotient-family divergence visible rather than concealed. - **Uvěrjenost / status:** 0.73 (medium); `provisional`; revision `OLISV-T0065-r0001`. - **Slovjanske sravnenja / comparanda:** ru: фактор-структура; uk: фактор-структура; pl: struktura ilorazowa; cs: faktorová struktura; bcs: kvocijentna struktura; bg: фактор-структура. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[6647]; dictionary_id=16781; lemma=faktor; gloss=factor); ISV-DICT-LIVE-20260825 (wordList[16426]; dictionary_id=16363; lemma=struktura; gloss=structure); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** kvocientna struktura: This is coherent with the existing quotient-set canon, but faktorna struktura more directly matches Open Logic's factor label and the inherited quotient use faktorna grupa.; faktor-struktura: The hyphenated calque is less morphologically integrated than the inherited agreeing-adjective pattern faktorna grupa. - **Neizvěstnost / uncertainty:** No bounded source directly attests the complete Interslavic compound faktorna struktura.; The dictionary factor lemma has a broad causal or multiplicative sense and does not itself establish the quotient sense.; Cross-Slavic technical usage divides between factor-family and quotient-family terminology. ## OLISV-T0391 · model-theory.finite-standard-distance - **English lemma / sense:** finite standard distance — Distance between two model elements measured by a finite standard number of successor or predecessor steps; it determines membership in one block. - **Medžuslovjansky:** `konečno standardno råzstojańje`; lemma `konečno standardno råzstojańje`; neuter adjective phrase with noun. - **Upotrěbljenje / inflection:** Both adjectives agree in neuter singular with råzstojańje; use na konečnom standardnom råzstojańju after the locative preposition. - **Kirilična forma:** `конечно стандардно разстојанје` - **Argumentacija / rationale:** The phrase mirrors the three semantic restrictions in the source and chooses dictionary-backed råzstojańje over competing South-Slavic distance nouns, while preserving the accepted edition spelling konečny. - **Uvěrjenost / status:** 0.86 (high); `provisional`; revision `OLISV-T0391-r0001`. - **Slovjanske sravnenja / comparanda:** ru: конечное стандартное расстояние; uk: скінченна стандартна відстань; pl: skończona standardowa odległość; cs: konečná standardní vzdálenost; bcs: konačna standardna udaljenost; коначно стандардно растојање; bg: крайно стандартно разстояние. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[5457]; dictionary_id=21782; lemma=råzstojańje; gloss=distance); ISV-DICT-LIVE-20260825 (wordList[16187]; dictionary_id=20754; lemma=standardny; gloss=standard); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic and standard flavorization) - **Alternativy / alternatives:** konečny standardny odmak: Odmak is regionally legible but less cross-Slavically convergent than the dictionary-selected råzstojańje family.; standardna udaljenost: Dropping finite would incorrectly include non-standardly many successor steps and collapse distinct blocks. - **Neizvěstnost / uncertainty:** The frozen dictionary has no specialist row for the complete three-word model-theoretic phrase. ## OLISV-T0336 · model-theory.incomplete-material - **English lemma / sense:** incomplete — Not yet containing all material needed for the model-theory part to serve its intended expository function; an editorial-development status, not metalogical incompleteness. - **Medžuslovjansky:** `nepȯlny`; lemma `nepȯlny`; adjective. - **Upotrěbljenje / inflection:** Agree with the head noun: nepȯlny material, nepȯlna čęst, nepȯlno izloženje. Running standard-flavor prose may use nepolne; do not use this entry for logical incompleteness. - **Kirilična forma:** `неполны` - **Argumentacija / rationale:** The directly pinned native full-family head maximizes East/West/South transparency and describes unfinished coverage without importing the formal property of incompleteness. - **Uvěrjenost / status:** 0.94 (high); `provisional`; revision `OLISV-T0336-r0001`. - **Slovjanske sravnenja / comparanda:** ru: неполный; uk: неповний; pl: niepełny, niekompletny; cs: neúplný; bcs: nepotpun; непотпун, некомплетан, мањкав; bg: непълен. - **Dokazy / evidence:** OL-MODEL-THEORY-PART (lines 10-13); ISV-DICT-LIVE-20260825 (wordList[9107]; dictionary_id=28465; lemma=nepȯlny; gloss=incomplete, not full); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** nekompletny: The international loan is intelligible but less pan-Slavically native and may suggest a defective object rather than work still needing content. - **Neizvěstnost / uncertainty:** The term must remain separate from logical incompleteness and incompleteness theorems. ## OLISV-T0183 · model-theory.intended-structure - **English lemma / sense:** intended structure — A structure belonging to the class that an axiomatic theory is meant to describe, contrasted with unintended structures that also satisfy its axioms. - **Medžuslovjansky:** `naměrjena struktura`; lemma `naměrjena struktura`; feminine noun phrase. - **Upotrěbljenje / inflection:** The passive adjective naměrjena agrees with feminine struktura; use plural naměrjene struktury and locative plural v naměrjenyh strukturah. - **Kirilična forma:** `намєрјена структура` - **Argumentacija / rationale:** Naměrjena struktura makes the theory's descriptive intent explicit and is reconstructible from directly frozen intent, negative-participle, and structure evidence. It avoids zamysljena, whose direct dictionary head primarily means pensive or thoughtful, while remaining transparent to South and West Slavic readers. - **Uvěrjenost / status:** 0.74 (medium); `provisional`; revision `OLISV-T0183-r0001`. - **Slovjanske sravnenja / comparanda:** ru: предполагаемая структура; uk: передбачувана структура; pl: zamierzona struktura; cs: zamýšlená struktura; bcs: namjeravana struktura; bg: предвидена структура. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[9400,9404]; dictionary_id=9402,36965; lemma=naměr,naměrny; gloss=intention/plan,intentional/intended); ISV-DICT-LIVE-20260825 (wordList[18006]; dictionary_id=32623; lemma=nenaměrny, nenaměrjeny; gloss=unintentional, unintended); ISV-DICT-LIVE-20260825 (wordList[16426]; dictionary_id=16363; lemma=struktura; gloss=structure); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** zamysljena struktura: The phrase is readily understood in several Slavic languages, but the frozen positive adjective zamysljeny is glossed primarily as pensive or thoughtful; naměrjena better isolates the intended-as-designed sense needed here. - **Neizvěstnost / uncertainty:** No frozen row directly attests the positive full specialist phrase naměrjena struktura.; National model-theory traditions vary between intended, presumed, envisaged, and designated semantic nuances. ## OLISV-T0400 · model-theory.interpolation-theorem - **English lemma / sense:** interpolation theorem — Craig's interpolation theorem: if a sentence entails another, an interpolant can be expressed using only their common nonlogical vocabulary. - **Medžuslovjansky:** `teorema interpolacije`; lemma `teorema interpolacije`; feminine noun with genitive complement. - **Upotrěbljenje / inflection:** Teorema inflects as a feminine noun; interpolacije remains the genitive singular complement. Craigova teorema interpolacije is the explicit named variant used when attribution must be visible. - **Kirilična forma:** `теорема интерполације` - **Argumentacija / rationale:** Teorema interpolacije transparently combines the established canon head teorema with the internationally shared interpolation stem. Russian, Polish, Czech, and Croatian academic sources independently preserve that stem while varying between genitive, prepositional, adjectival, and possessive constructions. The genitive complement is compact, pan-Slavically legible, and matches the source's unattributed chapter title; Craigova teorema interpolacije remains the explicit named variant. - **Uvěrjenost / status:** 0.92 (high); `provisional`; revision `OLISV-T0400-r0001`. - **Slovjanske sravnenja / comparanda:** ru: теорема Крейга об интерполяции; uk: теорема Крейга про інтерполяцію; pl: Twierdzenie Craiga o interpolacji; cs: Craigova věta o interpolaci; bcs: Craigova interpolacija; Teorem (Craig); bg: теорема за интерполация. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (active canon=OLISV-T0273-r0001); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts) - **Alternativy / alternatives:** interpolacijska teorema: Readable, but the adjective is less directly aligned with the strong cross-Slavic genitive/prepositional evidence and can suggest a broader theorem class.; teorema o interpolaciji: Close to Russian and Czech/Polish prepositional patterns, but longer than the equally transparent genitive construction selected for the chapter heading.; Craigova teorema interpolacije: Mathematically exact and retained as the explicit named variant, but the Open Logic chapter title deliberately omits Craig's name. - **Neizvěstnost / uncertainty:** The source title is generic although the chapter develops Craig's theorem; the named variant is recorded for downstream occurrences.; No official Interslavic dictionary head for interpolacija is pinned; the selected internationalism is supported by four academic Slavic traditions and remains reversible. ## OLISV-T0018 · model-theory.interpretation - **English lemma / sense:** interpretation — An assignment of semantic values or denotations to the non-logical symbols of a language. - **Medžuslovjansky:** `interpretacija`; lemma `interpretacija`; feminine noun. - **Upotrěbljenje / inflection:** Feminine noun; genitive singular interpretacije. Use interpretacija simbola or interpretacija jezyka; do not substitute this automatically for every occurrence of structure. - **Kirilična forma:** `интерпретација` - **Argumentacija / rationale:** Interpretacija is directly supported and aligns with the international technical vocabulary in five of the six comparison traditions; Bulgarian divergence is recorded rather than hidden. - **Uvěrjenost / status:** 0.92 (high); `seed_preferred`; revision `OLISV-T0018-r0001`. - **Slovjanske sravnenja / comparanda:** ru: интерпретация; uk: інтерпретація; pl: interpretacja; cs: interpretace; bcs: interpretacija, tumačenje; bg: тълкуване. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[9458]; dictionary_id=4988); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** iztolkovanje: A native-rooted ‘explanation/interpretation’ alternative may be stylistically useful, but no direct bounded specialist lemma evidence was located. - **Neizvěstnost / uncertainty:** The Czech dictionary column contains an apparent spelling error; the comparandum records the normalized form and explicitly labels that normalization. ## OLISV-T0340 · model-theory.introduction - **English lemma / sense:** introduction — Introductory exposition that orients readers to the model-theory material before detailed development. - **Medžuslovjansky:** `vvedenje`; lemma `vvedeńje`; neuter noun. - **Upotrěbljenje / inflection:** Genitive singular and nominative plural vvedeńja. The dictionary head preserves its marked notation; the preferred running surface is normalized vvedenje/vvedenja so the official Cyrillic projector can distinguish ordinary nj from the protected ńj boundary. - **Kirilična forma:** `введење` - **Argumentacija / rationale:** The exact introduction head is unambiguous; the pinned row documents divergent but recognizable West/South counterparts. The dictionary lemma remains visible while the preferred running surface uses the standard-flavor spelling required for deterministic projection. - **Uvěrjenost / status:** 0.86 (high); `provisional`; revision `OLISV-T0340-r0001`. - **Slovjanske sravnenja / comparanda:** ru: введение; uk: вступ; pl: wprowadzenie; cs: úvod; bcs: uvod; увод; bg: въведение. - **Dokazy / evidence:** OL-MODEL-THEORY-PART (line 14); ISV-DICT-LIVE-20260825 (wordList[9507]; dictionary_id=3685; lemma=vvedeńje; gloss=introduction); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** vvod: The alternative also means preface and is broader than the explanatory introduction required here. - **Neizvěstnost / uncertainty:** National forms divide between vved- and uvod families; the selection is a reversible edition compromise. ## OLISV-T0088 · model-theory.lowenheim-skolem-theorem - **English lemma / sense:** Löwenheim–Skolem theorem — The family of first-order results relating satisfiable theories to models of controlled cardinality. - **Medžuslovjansky:** `teorema Lovenheima-Skolema`; lemma `teorema Lovenheima-Skolema`; feminine proper-name noun phrase. - **Upotrěbljenje / inflection:** The canonical machine surface is standard-Latin Lovenheima-Skolema; in running TeX write L\"owenheima--Skolema and display Löwenheima–Skolema in human-facing metadata. - **Kirilična forma:** `теорема Ловенхеима-Сколема` - **Argumentacija / rationale:** The genitive surname construction follows established edition usage and the dominant Slavic pattern for a named theorem. - **Uvěrjenost / status:** 0.86 (high); `provisional`; revision `OLISV-T0088-r0001`. - **Slovjanske sravnenja / comparanda:** ru: теорема Лёвенгейма–Сколема; uk: теорема Левенгейма–Сколема; pl: twierdzenie Löwenheima–Skolema; cs: Löwenheimova–Skolemova věta; bcs: Löwenheim–Skolemov teorem; bg: теорема на Льовенхайм–Сколем. - **Dokazy / evidence:** ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** teorema Löwenheim–Skolem: The uninflected English-style names break the edition's running Slavic grammar. - **Neizvěstnost / uncertainty:** The standard transliterator normalizes foreign ö to o in Cyrillic.; Upward and downward statements require separate later sense entries. ## OLISV-T0017 · model-theory.model - **English lemma / sense:** model; model of a set of sentences — A structure that satisfies a specified sentence, or every sentence in a specified set or theory. - **Medžuslovjansky:** `model`; lemma `model`; masculine noun. - **Upotrěbljenje / inflection:** Masculine noun; genitive singular modela, nominative plural modeli. Model množstva Γ is a structure satisfying every sentence in Γ; a model of one sentence or a theory is the corresponding special case. - **Kirilična forma:** `модел` - **Argumentacija / rationale:** The international lemma and all-language dictionary consensus remain unchanged. OLP-0169 gives the exact arbitrary-set definition, so this revision broadens the recorded sense rather than creating a duplicate term. - **Uvěrjenost / status:** 0.97 (high); `seed_preferred`; revision `OLISV-T0017-r0002`. - **Slovjanske sravnenja / comparanda:** ru: модель; uk: модель; pl: model; cs: model; bcs: model; bg: модел. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[11194]; dictionary_id=19859); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** vzor: Vzor denotes a pattern or exemplar and does not encode satisfaction of a formal theory. - **Neizvěstnost / uncertainty:** No specific uncertainty beyond the provisional edition boundary. ## OLISV-T0365 · model-theory.models-of-arithmetic - **English lemma / sense:** models of arithmetic — Structures that interpret an arithmetic language or satisfy an arithmetic theory, including standard, non-standard, Q, PA, and computable models in the chapter scope. - **Medžuslovjansky:** `modeli aritmetiky`; lemma `modeli aritmetiky`; masculine plural noun phrase with feminine genitive-singular complement. - **Upotrěbljenje / inflection:** Singular model aritmetiky; plural modeli aritmetiky; genitive plural modelov aritmetiky. Retain aritmetiky as the complement rather than turning it into an adjective. - **Kirilična forma:** `модели аритметикы` - **Argumentacija / rationale:** Modeli aritmetiky is the shortest transparent Interslavic rendering of the Open Logic chapter head. It composes the established canon head model (OLISV-T0017) with the directly attested aritmetika component already used in OLISV-T0187 and OLISV-T0205. The genitive complement matches Russian, Ukrainian, Polish, Czech, and Bosnian/Croatian/Serbian structure, while Bulgarian independently confirms the same semantic relation analytically. The phrase preserves the distinction between a plurality of structures and arithmetic as either language or theory. - **Uvěrjenost / status:** 0.97 (high); `provisional`; revision `OLISV-T0365-r0001`. - **Slovjanske sravnenja / comparanda:** ru: модели арифметики; uk: моделі арифметики; pl: modele arytmetyki; cs: modely aritmetiky; bcs: modeli aritmetike; модели аритметике; bg: модели на аритметиката. - **Dokazy / evidence:** OL-MODEL-ARITHMETIC-CHAPTER-DRIVER (line 8 and ordered imports on lines 10-20); ISV-DICT-LIVE-20260825 (wordList[11194]; dictionary_id=19859; lemma=model; gloss=model); ISV-DICT-LIVE-20260825 (wordList[1093]; dictionary_id=21256; lemma=aritmetika; gloss=arithmetics); ISV-TRANSLIT-3.4.4 (package/dist/index.browser.min.js; isv-Cyrl) - **Alternativy / alternatives:** aritmetične modeli: The adjective can suggest models used for calculation or models having merely arithmetic properties, while the genitive construction more clearly preserves the source relation and dominates the comparison traditions.; modeli aritmetičnoj teorije: This is too narrow because the chapter includes structures, languages, standard and non-standard models, Q, PA, and computability rather than one single arithmetic theory. - **Neizvěstnost / uncertainty:** The complete specialist phrase is a transparent project-house composition of directly attested official Interslavic components rather than a standalone official dictionary headword.; Arithmetic is intentionally left broad between language and theory at chapter level; child units will narrow the sense where Open Logic does. ## OLISV-T0341 · model-theory.motivation - **English lemma / sense:** motivation — Exposition explaining why the model-theory topics and results matter and why they are introduced. - **Medžuslovjansky:** `motivacija`; lemma `motivacija`; feminine abstract noun. - **Upotrěbljenje / inflection:** Genitive singular motivacije and nominative plural motivacije; use motivacija za with an accusative complement. - **Kirilična forma:** `мотивација` - **Argumentacija / rationale:** The direct lemma is transparent and completely convergent across the comparison traditions. - **Uvěrjenost / status:** 0.99 (high); `provisional`; revision `OLISV-T0341-r0001`. - **Slovjanske sravnenja / comparanda:** ru: мотивация; uk: мотивація; pl: motywacja; cs: motivace; bcs: motivacija; мотивација; bg: мотивация. - **Dokazy / evidence:** OL-MODEL-THEORY-PART (line 14); ISV-DICT-LIVE-20260825 (wordList[11366]; dictionary_id=646; lemma=motivacija; gloss=motivation); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** motiv: Motiv means a motive rather than the pedagogical explanatory material requested by the source. - **Neizvěstnost / uncertainty:** The entry is bounded to pedagogical motivation in this source. ## OLISV-T0358 · model-theory.n-elementary-equivalence - **English lemma / sense:** n-equivalence — Agreement of two structures on the truth of every sentence whose quantifier rank is at most n. - **Medžuslovjansky:** `n-elementarna ekvivalentnost`; lemma `n-elementarna ekvivalentnost`; feminine indexed adjective-noun phrase. - **Upotrěbljenje / inflection:** Feminine ekvivalentnost; structures are n-elementarno ekvivalentne. Retain the index n as a mathematical metavariable in typeset prose even though the deterministic plain-text Cyrillic head projects its letter. - **Kirilična forma:** `н-елементарна еквивалентност` - **Argumentacija / rationale:** N-elementarna ekvivalentnost explicitly connects the bounded notion to OLISV-T0351 elementarna ekvivalentnost and matches the direct Polish and Croatian indexed terms. The qualifier prevents confusion with game n-equivalence, which the Russian syllabus explicitly distinguishes. The source's shorter English n-equivalent label remains searchable in the English field and definition. - **Uvěrjenost / status:** 0.94 (high); `provisional`; revision `OLISV-T0358-r0001`. - **Slovjanske sravnenja / comparanda:** ru: формульная n-эквивалентность; модели n-эквивалентны; uk: n-елементарна еквівалентність; pl: m-elementarna równoważność; cs: n-elementární ekvivalence; bcs: n-elementarna ekvivalentnost; bg: n-елементарна еквивалентност. - **Dokazy / evidence:** OL-MODEL-PARTIAL-ISOMORPHISM (lines 116-124 and 248-261); RU-HSE-QUANTIFIER-RANK-N-EQUIVALENCE-2018 (physical PDF pages 2-3, items 45-49); PL-UW-PARTIAL-ISOMORPHISM-QUANTIFIER-RANK-N-EQUIVALENCE (physical/printed PDF page 4, Definition 13); HR-ZAGREB-PARTIAL-ISOMORPHISM-QUANTIFIER-RANK-N-EQUIVALENCE (physical PDF page 124, printed page 116); ISV-DICT-LIVE-20260825 (dictionary_id=36133; ekvivalentny; plus established OLISV-T0351 elementary-equivalence components); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; Standard Cyrillic) - **Alternativy / alternatives:** n-ekvivalentnost: This literal rendering is short and directly resembles Russian usage, but without elementarna it can be confused with game, formula, algebraic, or other indexed equivalences.; formulna n-ekvivalentnost: The Russian qualifier is precise, but the Open Logic definition applies to structures via sentences, while Polish and Croatian directly anchor the notion in elementary equivalence. - **Neizvěstnost / uncertainty:** The English source says n-equivalent without elementary, while the Polish and Croatian direct terms include the elementary qualifier.; The deterministic Cyrillic dictionary head transliterates the plain-text metavariable n; mathematical typesetting retains Latin n. ## OLISV-T0380 · model-theory.nonstandard-arithmetic-structure - **English lemma / sense:** non-standard arithmetic structure — A structure for the first-order language of arithmetic that is not isomorphic to the distinguished natural-number structure, whether or not it satisfies a specified arithmetic theory. - **Medžuslovjansky:** `nestandardna struktura za jezyk aritmetiky`; lemma `nestandardna struktura za jezyk aritmetiky`; feminine noun phrase with prepositional complement. - **Upotrěbljenje / inflection:** Use short nestandardna struktura when the arithmetic-language context is explicit. Reserve nestandardny model aritmetiky for a structure known to satisfy the relevant arithmetic theory. - **Kirilična forma:** `нестандардна структура за језык аритметикы` - **Argumentacija / rationale:** The explicit language complement prevents model from being used before satisfaction has been established. It also makes the source's integer-domain counterexample readable without falsely calling that structure a model of true arithmetic. - **Uvěrjenost / status:** 0.9 (high); `provisional`; revision `OLISV-T0380-r0001`. - **Slovjanske sravnenja / comparanda:** ru: нестандартная структура языка арифметики; uk: нестандартна структура мови арифметики; pl: niestandardowa struktura języka arytmetyki; cs: nestandardní struktura pro aritmetický jazyk; bcs: nestandardna struktura jezika aritmetike; bg: нестандартна структура на езика на аритметиката. - **Dokazy / evidence:** OL-MODEL-ARITHMETIC-NONSTANDARD-MODELS (lines 13-23 and 67-75); ISV-DICT-LIVE-20260825 (wordList[11792,16426,9987,1093]; dictionary_id=37954,16363,541,21256); PL-UW-MATHEMATICAL-LOGIC-2014-15 (printed page 21 / extracted lines 1032-1057); HR-ZAGREB-CLASSICAL-LOGIC-2013 (physical page 66 / extracted lines 65-72); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic, standard flavorization) - **Alternativy / alternatives:** nestandardny model aritmetiky: This stronger term asserts modelhood and is false of the source's integer-domain example.; nestandardna aritmetika: This can denote a discipline or theory rather than a structure interpreting the arithmetic language. - **Neizvěstnost / uncertainty:** The full phrase is a transparent edition compound rather than a standalone official dictionary headword. ## OLISV-T0369 · model-theory.nonstandard-element - **English lemma / sense:** non-standard element — An element of an arithmetic-language structure that is not the value of any standard numeral; when the numerical role is foregrounded, the same kind of object is called a non-standard number. - **Medžuslovjansky:** `nestandardny element`; lemma `nestandardny element`; masculine adjective-noun phrase. - **Upotrěbljenje / inflection:** Masculine singular nestandardny element; plural nestandardne elementy; locative plural o nestandardnyh elementah. - **Kirilična forma:** `нестандардны елемент` - **Argumentacija / rationale:** The existing nestandardny element remains the general head, but OLP-0194 shows that the definition applies to arbitrary structures for the arithmetic language, not only to models of true arithmetic. The revision removes that accidental model-only restriction while keeping the number-focused term separate. - **Uvěrjenost / status:** 0.91 (high); `provisional`; revision `OLISV-T0369-r0002`. - **Slovjanske sravnenja / comparanda:** ru: нестандартный элемент; uk: нестандартний елемент; pl: element niestandardowy; cs: nestandardní prvek; bcs: nestandardni element; bg: нестандартен елемент. - **Dokazy / evidence:** OL-MODEL-ARITHMETIC-NONSTANDARD-MODELS (lines 19-36); ISV-DICT-LIVE-20260825 (wordList[11792,6006]; dictionary_id=37954,17372); UK-KNU-MODEL-THEORY-2023 (physical page 165 / decoded lines 8752-8756); HR-ZAGREB-CLASSICAL-LOGIC-2013 (physical page 66 / extracted lines 69-72); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic, standard flavorization) - **Alternativy / alternatives:** nestandardno čislo: This is valid for the arithmetic example but too narrow for the generic element occurrences and for later structures whose domain need not be presented as numbers.; neobyčny element: It expresses unusualness rather than failure to equal every standard numeral value. - **Neizvěstnost / uncertainty:** National traditions vary between element and number depending on whether structure membership or numerical order is foregrounded.; This revision broadens the source class; it does not claim that every non-standard arithmetic structure is a model of an arithmetic theory. ## OLISV-T0368 · model-theory.nonstandard-model - **English lemma / sense:** non-standard model — A model of the relevant true arithmetic theory that is not isomorphic to the standard natural-number structure. - **Medžuslovjansky:** `nestandardny model aritmetiky`; lemma `nestandardny model aritmetiky`; masculine adjective-noun phrase. - **Upotrěbljenje / inflection:** Full canon head nestandardny model aritmetiky; plural nestandardne modeli aritmetiky; locative plural v nestandardnyh modelah aritmetiky. The shorter nestandardny model is allowed only where the arithmetic scope is already explicit. - **Kirilična forma:** `нестандардны модел аритметикы` - **Argumentacija / rationale:** Nestandardny model aritmetiky composes three directly listed Interslavic heads and mirrors the strongest Ukrainian and Polish full specialist phrases while remaining compatible with Czech and Croatian contextual short forms. Naming arithmetic in the canon head fixes the domain even when the term is indexed outside its local paragraph; prose may shorten it only after that scope is explicit. - **Uvěrjenost / status:** 0.97 (high); `provisional`; revision `OLISV-T0368-r0001`. - **Slovjanske sravnenja / comparanda:** ru: нестандартная модель арифметики; uk: нестандартна модель арифметики; pl: niestandardowy model arytmetyki; cs: nestandardní model; bcs: nestandardni model aritmetike; bg: нестандартен модел на аритметиката. - **Dokazy / evidence:** OL-MODEL-ARITHMETIC-INTRODUCTION (lines 42-53); ISV-DICT-LIVE-20260825 (wordList[11792]; dictionary_id=37954; lemma=nestandardny; gloss=nonstandard); ISV-DICT-LIVE-20260825 (wordList[11194]; dictionary_id=19859; lemma=model; gloss=model); ISV-DICT-LIVE-20260825 (wordList[1093]; dictionary_id=21256; lemma=aritmetika; gloss=arithmetics); UK-KNU-MODEL-THEORY-2023 (physical page 37 / decoded lines 1810-1834); PL-UW-MATHEMATICAL-LOGIC-2014-15 (printed page 21 / extracted lines 1032-1057); HR-ZAGREB-CLASSICAL-LOGIC-2013 (physical pages 66-69 / extracted lines 69 and 121); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic, standard flavorization) - **Alternativy / alternatives:** nestandardny model: This remains acceptable as a context-bound short form, but as the standalone canon head it omits the arithmetic scope fixed by the strongest Ukrainian and Polish specialist witnesses.; neobyčny model: This means unusual rather than non-isomorphic to the standard arithmetic structure and therefore loses the technical boundary. - **Neizvěstnost / uncertainty:** The exact phrase remains an edition-level specialist selection rather than a separately certified Interslavic standard.; The candidate's bare nestandardny model occurrences are licensed contextual shortenings and do not replace the full indexed head. ## OLISV-T0395 · model-theory.nonstandard-part - **English lemma / sense:** non-standard part of a model — The non-standard elements of a model of arithmetic, partitioned into finite-standard-distance blocks. - **Medžuslovjansky:** `nestandardna čest modela`; lemma `nestandardna čest modela`; feminine adjective-noun phrase with genitive complement. - **Upotrěbljenje / inflection:** Nestandardna agrees with feminine čest; modela is genitive singular. In context the short form nestandardna čest is preferred once the model is explicit. - **Kirilična forma:** `нестандардна чест модела` - **Argumentacija / rationale:** The compound is transparent, parallels standardna čest, and is directly supported by the source construction plus a pinned Polish specialist occurrence of the non-standard part of an arithmetic structure. - **Uvěrjenost / status:** 0.93 (high); `provisional`; revision `OLISV-T0395-r0001`. - **Slovjanske sravnenja / comparanda:** ru: нестандартная часть модели; uk: нестандартна частина моделі; pl: niestandardowa część modelu; cs: nestandardní část modelu; bcs: nestandardni dio modela; нестандардни део модела; bg: нестандартна част на модела. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[12471]; dictionary_id=1731; lemma=čęsť; gloss=part); ISV-DICT-LIVE-20260825 (wordList[11792]; dictionary_id=37954; lemma=nestandardny); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic and standard flavorization) - **Alternativy / alternatives:** nestandardno podmnožstvo modela: The source uses the whole complementary region of the model and its block decomposition, not an arbitrary subset.; nestandardna zona modela: Zona adds a spatial metaphor absent from the source and has weaker specialist convergence than part. - **Neizvěstnost / uncertainty:** The Polish direct witness uses structure rather than model as its genitive complement; the source fixes the model-scoped use here. ## OLISV-T0350 · model-theory.overspill-compactness-corollary - **English lemma / sense:** overspill (compactness corollary) — The compactness consequence that a set of first-order sentences with arbitrarily large finite models also has an infinite model; here this is not the nonstandard-analysis overspill principle and not computing overflow. - **Medžuslovjansky:** `prěhod k bezkonečnosti`; lemma `prěhod k bezkonečnosti`; masculine noun phrase with dative complement. - **Upotrěbljenje / inflection:** Use the fixed section-title form prěhod k bezkonečnosti. Outside the title, inflect the head regularly (for example, genitive prěhoda) while keeping k plus dative bezkonečnosti. - **Kirilična forma:** `прєход к безконечности` - **Argumentacija / rationale:** The surveyed Ukrainian and Czech academic treatments present the result as a theorem or example derived from compactness, while the Polish and Croatian sources independently confirm the key finite-model and countably-many-constants wording. No stable cross-Slavic specialist calque of the source label was found in the bounded survey. Prěhod k bezkonečnosti therefore names the exact mathematical movement in transparent, dictionary-attested components and remains immediately parsable to Slavic-language readers without importing the misleading computing-overflow or nonstandard-analysis senses of overspill. - **Uvěrjenost / status:** 0.86 (high); `provisional`; revision `OLISV-T0350-r0001`. - **Slovjanske sravnenja / comparanda:** ru: переход к бесконечности; uk: перехід до нескінченності; pl: przejście do nieskończoności; cs: přechod k nekonečnu; bcs: prijelaz/prelaz ka beskonačnosti; пријелаз/прелаз ка бесконачности; bg: преход към безкрайността. - **Dokazy / evidence:** OL-MODEL-OVERSPILL (lines 11-42); ISV-DICT-LIVE-20260825 (wordList[17556]; dictionary_id=19506; lemma=prěhod; gloss=transition); ISV-DICT-LIVE-20260825 (wordList[9220]; dictionary_id=6519; lemma=bezkonėčnosť; gloss=infinity, perpetuality); UK-KNU-COMPACTNESS-INFINITE-MODEL-2023 (physical PDF page 95, printed page 94, Theorem 4.20); CS-CUNI-COMPACTNESS-INFINITE-MODEL (physical PDF page 32, printed page 31); PL-UW-ARBITRARILY-LARGE-FINITE-MODELS (physical PDF page 8, problem 12(b,d)); HR-ZAGREB-COUNTABLY-MANY-CONSTANTS (physical PDF page 25, printed page 19); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** prěpolnjenje: A literal spill/overflow calque would invite computing-overflow and unrelated logical-explosion senses, while the checked academic theorem sources do not use such a title.; overspill: Retaining the unexplained English label would be opaque to readers who do not know English and would collide with the better-known nonstandard-analysis principle; the source label remains recoverable from the English witness and canon key.; poslědstvo kompaktnosti: bezkonečny model: This is semantically exact and remains a documented explanatory alternative, but it reads as a synopsis rather than a concise section name and repeats terminology made explicit in the first theorem. - **Neizvěstnost / uncertainty:** The complete Interslavic title is a transparent editorial phrase, not a frozen dictionary headword or directly attested national specialist title.; The bounded survey supports absence of a stable cross-Slavic Overspill calque in the checked sources but cannot prove universal absence across all Slavic scholarship.; Prěhod k bezkonečnosti can be read more broadly outside this section; the canon key and theorem locator fix the compactness-corollary sense. ## OLISV-T0355 · model-theory.partial-isomorphism - **English lemma / sense:** partial isomorphism — A finite partial function between two structures that satisfies the isomorphism conditions wherever the function is defined. - **Medžuslovjansky:** `čestičny izomorfizm`; lemma `čestičny izomorfizm`; masculine adjective-noun phrase. - **Upotrěbljenje / inflection:** Masculine inanimate phrase; genitive singular čestičnogo izomorfizma and plural čestične izomorfizmy. The edition's simplified čestičny surface follows OLISV-T0037. - **Kirilična forma:** `честичны изоморфизм` - **Argumentacija / rationale:** Čestičny izomorfizm reuses the canon's established native partial adjective from OLISV-T0037 and the structure-isomorphism head from OLISV-T0352. Russian and Polish directly support the same native part-based family; Croatian supplies a directly attested international alternative. The definition, not superficial word similarity, fixes the finite partial-function sense. - **Uvěrjenost / status:** 0.91 (high); `provisional`; revision `OLISV-T0355-r0001`. - **Slovjanske sravnenja / comparanda:** ru: частичный изоморфизм; uk: частковий ізоморфізм; pl: częściowy izomorfizm; cs: částečný izomorfismus; bcs: parcijalni izomorfizam; bg: частичен изоморфизъм. - **Dokazy / evidence:** OL-MODEL-PARTIAL-ISOMORPHISM (lines 10-38); ISV-DICT-LIVE-20260825 (wordList entry dictionary_id=37394; čęstičny; gloss partial); RU-NSTU-PARTIAL-ISOMORPHISM-2011 (physical/printed PDF page 60); PL-UW-PARTIAL-ISOMORPHISM-QUANTIFIER-RANK-N-EQUIVALENCE (physical/printed PDF page 2, Definition 3); HR-ZAGREB-PARTIAL-ISOMORPHISM-QUANTIFIER-RANK-N-EQUIVALENCE (physical PDF page 20, printed page 12, Definition 1.21); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; Standard Cyrillic) - **Alternativy / alternatives:** parcialny izomorfizm: The international adjective is directly recognizable from Croatian, but it is less continuous with the already accepted čestičny mathematical family and the direct East/West Slavic evidence.; lokalny izomorfizm: Local isomorphism occurs in neighboring literature but can denote different germs or local structures and does not transparently assert a partial function. - **Neizvěstnost / uncertainty:** The official dictionary head is čęstičny; the edition uses the simplified čestičny surface already established by OLISV-T0037.; Russian and Polish use the native part-based adjective while Croatian uses the international parcijalni family. ## OLISV-T0359 · model-theory.purely-relational-language - **English lemma / sense:** purely relational language — A first-order language whose nonlogical vocabulary contains relation or predicate symbols but no function symbols, with the treatment of constants stated locally by the source. - **Medžuslovjansky:** `čisto relacijsky jezyk`; lemma `čisto relacijsky jezyk`; masculine adverb-adjective-noun phrase. - **Upotrěbljenje / inflection:** Masculine phrase; genitive čisto relacijskogo jezyka. The accompanying definition must state whether constants are excluded, because the source itself changes that convention between passages. - **Kirilična forma:** `чисто релацијскы језык` - **Argumentacija / rationale:** Čisto relacijsky jezyk is a transparent compositional label: čisto excludes nonrelational operations, relacijsky identifies the signature family, and jezyk remains the edition's ordinary language head. The entry records the source's deliberate local convention shift—one theorem excludes constants while a later finite-language proposition permits them—so the head is never used as a substitute for checking the adjacent definition. - **Uvěrjenost / status:** 0.84 (high); `provisional`; revision `OLISV-T0359-r0001`. - **Slovjanske sravnenja / comparanda:** ru: чисто реляционный язык; uk: суто реляційна мова; pl: czysto relacyjny język; cs: čistě relační jazyk; bcs: čisto relacijski jezik; bg: чисто релационен език. - **Dokazy / evidence:** OL-MODEL-PARTIAL-ISOMORPHISM (lines 83-108 and 126-138); ISV-DICT-LIVE-20260825 (dictionary_id=582 čisty; 541 język; established relation-family components); PL-UW-PARTIAL-ISOMORPHISM-QUANTIFIER-RANK-N-EQUIVALENCE (physical/printed PDF pages 2 and 4); HR-ZAGREB-PARTIAL-ISOMORPHISM-QUANTIFIER-RANK-N-EQUIVALENCE (physical PDF pages 20-21); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; Standard Cyrillic) - **Alternativy / alternatives:** bezfunkcijny jezyk: This describes the most important negative condition but hides the positive relational vocabulary and still leaves the status of constants ambiguous.; predikatny jezyk: Predicate language is recognizable but can be misread as the whole first-order language family and does not foreground the no-function restriction. - **Neizvěstnost / uncertainty:** The source itself excludes constants in its first purely relational theorem but permits constants in its later finite-language proposition.; The full phrase is a compositional edition choice; only its relational components are directly attested in the pinned Polish and Croatian sources. ## OLISV-T0357 · model-theory.quantifier-rank - **English lemma / sense:** quantifier rank — The maximum nesting depth of quantifiers in a formula, recursively defined as a natural number. - **Medžuslovjansky:** `kvantifikatorny rang`; lemma `kvantifikatorny rang`; masculine adjective-noun phrase. - **Upotrěbljenje / inflection:** Masculine inanimate phrase; genitive kvantifikatornogo ranga and instrumental kvantifikatornym rangom. Rank measures nesting depth, not social or matrix rank. - **Kirilična forma:** `квантификаторны ранг` - **Argumentacija / rationale:** Kvantifikatorny rang follows the convergent adjective-plus-rank structure directly attested in Russian, Polish, and Croatian while reusing the edition's established kvantifikator head. The adjectival form is more faithful to all three academic witnesses than an unexplained genitive paraphrase, and the definition explicitly limits the sense to quantifier nesting depth. - **Uvěrjenost / status:** 0.97 (high); `provisional`; revision `OLISV-T0357-r0001`. - **Slovjanske sravnenja / comparanda:** ru: кванторный ранг; uk: кванторний ранг; pl: ranga kwantyfikatorowa; cs: kvantifikátorový rang; bcs: kvantifikatorski rang; bg: кванторен ранг. - **Dokazy / evidence:** OL-MODEL-PARTIAL-ISOMORPHISM (lines 112-124); ISV-DICT-LIVE-20260825 (dictionary_id=16072; rang; gloss level; and OLISV-T0100's pinned kvantifikator source components); RU-HSE-QUANTIFIER-RANK-N-EQUIVALENCE-2018 (physical PDF page 2, item 45); PL-UW-PARTIAL-ISOMORPHISM-QUANTIFIER-RANK-N-EQUIVALENCE (physical/printed PDF page 3, Definition 10); HR-ZAGREB-PARTIAL-ISOMORPHISM-QUANTIFIER-RANK-N-EQUIVALENCE (physical PDF page 21, Definition 1.24); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; Standard Cyrillic) - **Alternativy / alternatives:** rang kvantifikatorov: The genitive phrase is transparent, but every pinned direct national witness uses an adjective and the edition already forms kvantifikatorny regularly.; glubina kvantifikatorov: Depth is explanatory but loses direct correspondence with the rank notation and the strongly convergent Slavic academic rank family. - **Neizvěstnost / uncertainty:** Russian commonly shortens quantifier to квантор in the compound, whereas the edition retains the already canonical full head kvantifikator.; Some Czech sources may prefer a depth term rather than the international rank family. ## OLISV-T0364 · model-theory.rational-order - **English lemma / sense:** rational order — The linear order carried by the rational numbers, considered as an order structure or order type rather than as a field. - **Medžuslovjansky:** `poredok racionaľnyh čisl`; lemma `poredok racionaľnyh čisl`; masculine noun phrase with genitive plural complement. - **Upotrěbljenje / inflection:** Use poredok racionaľnyh čisl or poredkovy tip struktury Q; avoid bare racionaľny poredok because it can be read as a reasonable order. - **Kirilična forma:** `поредок рационалных числ` - **Argumentacija / rationale:** The genitive construction names the mathematical carrier explicitly and reuses OLISV-T0253 for racionaľno čislo plus OLISV-T0038 for poredok. Polish and Croatian witnesses both present Q as the canonical order structure. This head prevents the adjective racionaľny from being misread in its ordinary sense of reasonable and prevents the order reduct from being confused with the rational field. - **Uvěrjenost / status:** 0.89 (high); `provisional`; revision `OLISV-T0364-r0001`. - **Slovjanske sravnenja / comparanda:** ru: порядок рациональных чисел; uk: порядок раціональних чисел; pl: porządek (Q, <=); cs: uspořádání racionálních čísel; bcs: uređaj skupa Q; bg: наредбата на рационалните числа. - **Dokazy / evidence:** OL-MODEL-DENSE-LINEAR-ORDER (lines 69-83); PL-PW-DENSE-LINEAR-ORDER-2022 (physical/printed PDF page 23, Zadanie 181); HR-ZAGREB-DENSE-LINEAR-ORDER-2015 (physical PDF page 52, printed page 48, Theorem 1.77); ISV-TRANSLIT-3.4.4 (package/dist/index.browser.min.js; isv-Cyrl) - **Alternativy / alternatives:** racionaľny poredok: The adjective can be read as reasonable or rationally chosen and does not state that the carrier is the set of rational numbers.; racionaľna struktura: This can denote the field or another structure on the rationals and therefore loses the order-reduct boundary. - **Neizvěstnost / uncertainty:** The selected Interslavic head is a transparent project-house compound rather than a directly attested official specialist dictionary entry.; Order-type notation eta may be added in a later unit if Open Logic introduces it explicitly; it is not silently imported here. ## OLISV-T0346 · model-theory.reduct - **English lemma / sense:** reduct — The structure obtained from a structure in a larger language by retaining the same domain and forgetting only the interpretations of symbols outside the smaller language. - **Medžuslovjansky:** `redukt`; lemma `redukt`; masculine noun. - **Upotrěbljenje / inflection:** Use nominative redukt, genitive redukta, instrumental reduktom, and nominative plural redukty. Reserve redukcija for the operation or process rather than the resulting structure. - **Kirilična forma:** `редукт` - **Argumentacija / rationale:** Redukt is the transparent result noun required by the Open Logic definition. Czech teaching material explicitly distinguishes redukce from the resulting redukt, and the Serbian model-theory witness uses redukt in the same restriction-to-a-smaller-language construction. The frozen dictionary confirms the reduk- family across all comparison regions. This is therefore more precise than using redukcija for both process and object. - **Uvěrjenost / status:** 0.89 (high); `provisional`; revision `OLISV-T0346-r0001`. - **Slovjanske sravnenja / comparanda:** ru: редукция; uk: редукція; pl: redukcja; cs: redukt; redukce; bcs: redukt; redukcija; редукт; редукција; bg: редукция. - **Dokazy / evidence:** OL-MODEL-REDUCTS-EXPANSIONS (lines 24-39; definition defn:reduct); ISV-DICT-LIVE-20260825 (wordList[14072]; dictionary_id=30601; lemma=redukcija; gloss=reduction); CS-VPL-REDUCT-EXPANSION (physical PDF page 71, printed slides 35-40: redukce struktury; redukt M = M'|L); SR-KG-REDUCT-EXPANSION-2013 (physical PDF page 74, printed page 69: Ako je A redukt od A* na L); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** redukcija struktury: The dictionary-attested noun primarily names the reduction process; using it for the resulting structure would erase the process-versus-object distinction explicitly visible in Czech specialist usage.; ograničena struktura: A restricted-structure paraphrase is understandable but risks confusion with restriction, substructure, or boundedness and lacks the concise specialist symmetry with razširjenje. - **Neizvěstnost / uncertainty:** The pinned Interslavic dictionary contains redukcija but no direct redukt headword; redukt is therefore a specialist editorial formation rather than a claimed general-standard lemma.; Direct exact-sense evidence is strongest in Czech and Serbian; other comparison columns currently establish the root family rather than the complete model-theory term. ## OLISV-T0202 · model-theory.relation-expression - **English lemma / sense:** formula expressing a relation — The satisfaction-relative condition in which a formula with specified free variables holds under exactly those assignments whose values stand in a given relation. - **Medžuslovjansky:** `izražanje odnošenja formulom`; lemma `izražanje odnošenja formulom`; neuter verbal noun phrase. - **Upotrěbljenje / inflection:** Neuter head izražanje with genitive odnošenja and instrumental formulom; in clauses use formula izražaje odnošenje. - **Kirilična forma:** `изражање одношења формулом` - **Argumentacija / rationale:** The phrase preserves the source's distinction between a formula expressing a relation and the broader model-theoretic concept of definability. All three lexical components are directly registered and the controlled clause states the formal operation naturally. - **Uvěrjenost / status:** 0.91 (high); `provisional`; revision `OLISV-T0202-r0001`. - **Slovjanske sravnenja / comparanda:** ru: выражение отношения формулой; uk: вираження відношення формулою; pl: wyrażanie relacji formułą; cs: vyjádření relace formulí; bcs: izražavanje relacije formulom; изражавање релације формулом; bg: изразяване на отношение с формула. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[6564]; dictionary_id=682; lemma=izražati; gloss=express); ISV-DICT-LIVE-20260825 (wordList[7255]; dictionary_id=5181; lemma=formula; gloss=formula); ISV-DICT-LIVE-20260825 (wordList[14174]; dictionary_id=1992; lemma=odnošeńje; gloss=relation); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** definovanje odnošenja: This collapses expression into the broader definability concept and obscures the assignment-relative satisfaction condition that the source defines first. - **Neizvěstnost / uncertainty:** The complete verbal-noun phrase is editorial packaging; the controlled clause formula izražaje odnošenje is the primary running-prose form. ## OLISV-T0063 · model-theory.saturated-set - **English lemma / sense:** saturated set — A formula set containing a constant witness for each existential formula in the set. - **Medžuslovjansky:** `nasyćeno množstvo`; lemma `nasyćeno množstvo`; neuter noun phrase. - **Upotrěbljenje / inflection:** The past passive participle nasyćeny agrees with množstvo; use neuter singular nasyćeno množstvo and abstract noun nasyćenost. - **Kirilična forma:** `насычено множство` - **Argumentacija / rationale:** Nasyćeno množstvo preserves the widely recognizable Slavic saturation root, uses the official participial formation, and directly mirrors the defined property of having enough witnesses; the technical definition prevents the everyday satiation sense from carrying the analysis. - **Uvěrjenost / status:** 0.8 (high); `provisional`; revision `OLISV-T0063-r0001`. - **Slovjanske sravnenja / comparanda:** ru: насыщенное множество; uk: насичена множина; pl: zbiór nasycony; cs: nasycená množina; bcs: zasićen skup; bg: наситено множество. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[14814-14816]; dictionary_id=28260,28262,28261); ISV-GRAMMAR-VERBS (lines 180-182); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard flavorization ć→č before StandardCyrillic type=5) - **Alternativy / alternatives:** saturirano množstvo: The international loan is recognizable to specialists but is less directly parsable across the target readership than the strongly attested native saturation family. - **Neizvěstnost / uncertainty:** The dictionary attests the lexical family rather than the exact model-theoretic compound; the phrase remains an explicitly documented edition-level composition. ## OLISV-T0339 · model-theory.scholarly-notes - **English lemma / sense:** notes — Authored scholarly teaching or lecture notes serving as the source from which the model-theory material was adapted. - **Medžuslovjansky:** `zapiska`; lemma `zapiska`; feminine noun. - **Upotrěbljenje / inflection:** Genitive singular zapisky and nominative plural zapisky; the source genitive plural is zapisok. - **Kirilična forma:** `записка` - **Argumentacija / rationale:** The direct nonmusical note head is broadly recognizable; source syntax supplies the collected scholarly-notes reading. - **Uvěrjenost / status:** 0.88 (high); `provisional`; revision `OLISV-T0339-r0001`. - **Slovjanske sravnenja / comparanda:** ru: записка, заметка, примечание; uk: примітка, записка, замітка; pl: notatka; cs: poznámka, zápis; bcs: bilješka, zabilješka, zapis, napomena; запис, белешка, напомена; bg: записка, бележка, напомнянка. - **Dokazy / evidence:** OL-MODEL-THEORY-PART (lines 11-12); ISV-DICT-LIVE-20260825 (wordList[11846]; dictionary_id=6251; lemma=zapiska; gloss=note); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** nota: The pinned nota entry is restricted to a musical note and would change the source sense. - **Neizvěstnost / uncertainty:** The lemma can denote an individual note; the authored-document reading depends on source context and plural syntax. ## OLISV-T0243 · model-theory.second-order-part - **English lemma / sense:** second-order part — For each arity, the family of relations assigned to the second-order variables of a second-order structure. - **Medžuslovjansky:** `čest drugogo reda`; lemma `čest drugogo reda`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive česti drugogo reda; use čest to mean a component/part, not a mathematical set. - **Kirilična forma:** `чест другого реда` - **Argumentacija / rationale:** Čest is used as an explanatory component label because the source explicitly decomposes a structure into parts. It avoids inventing a new carrier/domain sense while keeping the relation family visible. - **Uvěrjenost / status:** 0.66 (medium); `provisional`; revision `OLISV-T0243-r0002`. - **Slovjanske sravnenja / comparanda:** ru: вторая часть структуры; uk: друга частина структури; pl: część drugiego rzędu; cs: druhořádová část; bcs: dio drugog reda; део другог реда; bg: част от втори ред. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (dictionary_id=35935; lemma=semantika; gloss=semantics); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** domen drugogo reda: Would conflate the family of relations with the domain term already reserved for carriers.; podstruktura: Suggests a substructure with inherited operations, which the source does not assert. - **Neizvěstnost / uncertainty:** Some traditions call this a relation sort, Henkin component, or second-order range; no single frozen headword is claimed.; The r0001 record remains preserved as adverse provenance for the target/source locator mismatch. ## OLISV-T0171 · model-theory.skolem-theorem - **English lemma / sense:** Skolem's theorem — The first-order Skolemization result used here: a formula of the form for every x there exists y A(x,y) is satisfiable exactly when an expansion with a fresh function symbol satisfies for every x A(x,f(x)). - **Medžuslovjansky:** `teorema Skolema`; lemma `teorema Skolema`; feminine proper-name noun phrase. - **Upotrěbljenje / inflection:** Genitive teoremy Skolema. Keep the genitive surname construction aligned with teorema Lovenheima-Skolema (OLISV-T0088); do not conflate this specific Skolemization result with that different named theorem. - **Kirilična forma:** `теорема Сколема` - **Argumentacija / rationale:** The genitive surname construction is already established by OLISV-T0088 and is directly intelligible across the comparison traditions; the separate canon ID prevents accidental identification of Skolemization with the Löwenheim–Skolem theorem. - **Uvěrjenost / status:** 0.87 (high); `provisional`; revision `OLISV-T0171-r0001`. - **Slovjanske sravnenja / comparanda:** ru: теорема Сколема; uk: теорема Сколема; pl: twierdzenie Skolema; cs: Skolemova věta; bcs: Skolemov teorem; Сколемова теорема; bg: теорема на Сколем. - **Dokazy / evidence:** ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** Skolemova teorema: The possessive adjective is grammatical and common in several traditions, but the genitive construction matches the edition's existing named-theorem policy and reduces competing surname paradigms. - **Neizvěstnost / uncertainty:** The label Skolem's theorem is used for several related results in the literature; the canon sense is restricted to the exact statement in the pinned Open Logic unit.; No frozen dictionary row directly attests the proper-name phrase. ## OLISV-T0205 · model-theory.standard-arithmetic-model - **English lemma / sense:** standard model of arithmetic — The natural-number structure N with the ordinary interpretations of the arithmetic vocabulary, or any L_A-structure isomorphic to it. Standardness is therefore invariant under isomorphism and does not assert that another model's domain elements are literally numbers. - **Medžuslovjansky:** `standardny model aritmetiky`; lemma `standardny model aritmetiky`; masculine noun phrase with genitive complement. - **Upotrěbljenje / inflection:** Masculine phrase; genitive standardnogo modela aritmetiky and locative v standardnom modelu aritmetiky. - **Kirilična forma:** `стандардны модел аритметикы` - **Argumentacija / rationale:** The surface remains unchanged because its three components are transparent and strongly convergent. Revision 2 repairs the sense boundary: this unit defines every structure isomorphic to N as standard, so the canon may not restrict the head to N alone or identify an isomorphic domain's objects literally with natural numbers. - **Uvěrjenost / status:** 0.98 (high); `provisional`; revision `OLISV-T0205-r0002`. - **Slovjanske sravnenja / comparanda:** ru: стандартная модель арифметики; uk: стандартна модель арифметики; pl: standardowy model arytmetyki; cs: standardní model aritmetiky; bcs: standardni model aritmetike; стандардни модел аритметике; bg: стандартен модел на аритметиката. - **Dokazy / evidence:** OL-MODEL-ARITHMETIC-STANDARD-MODELS (lines 12-23 and 43-50); ISV-DICT-LIVE-20260825 (wordList[16187,11194,1093]; dictionary_id=20754,19859,21256); RU-MI-RAS-PROVABILITY-ARITHMETIC-2020 (physical page 1 / extracted lines 26-28); UK-KNU-MODEL-THEORY-2023 (physical page 37 / decoded extract lines 1810-1815); CS-CUNI-LOGIC-II-2008 (physical page 1 / extracted lines 23-30); HR-ZAGREB-GODEL-INCOMPLETENESS-2011 (printed page 4 / physical page 6 / extracted lines 172-193); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic, standard flavorization) - **Alternativy / alternatives:** standardny model označaje jedino Struct N: This is the previous sense's over-narrow implication. OLP-0193 explicitly includes every structure isomorphic to N.; obyčny model aritmetiky: Ordinary suggests typicality and loses the conventional model-theoretic reference class fixed by isomorphism. - **Neizvěstnost / uncertainty:** The phrase is an edition-wide provisional technical head, not a claim of official Interslavic or native-speaker certification.; A standard model may have a domain whose elements are not literally natural numbers; only the arithmetic structure up to isomorphism is asserted. ## OLISV-T0370 · model-theory.standard-numeral - **English lemma / sense:** standard numeral — The canonical arithmetic-language term denoting an ordinary natural number, whose value exhausts the standard model but not a non-standard model. - **Medžuslovjansky:** `standardny numeral`; lemma `standardny numeral`; masculine adjective-noun phrase. - **Upotrěbljenje / inflection:** Masculine singular standardny numeral; plural standardne numeraly; genitive plural standardnyh numeralov. Numeral is reserved here for a formal-language term, not the grammatical part of speech. - **Kirilična forma:** `стандардны нумерал` - **Argumentacija / rationale:** Standardny numeral retains the international formal-logic noun directly attested in Russian and Czech and combines it with the official Interslavic adjective standardny. This deliberately avoids borrowing čislovnik from a dictionary row whose national columns overwhelmingly encode the grammatical word-class sense rather than an arithmetic-language term. - **Uvěrjenost / status:** 0.74 (medium); `provisional`; revision `OLISV-T0370-r0001`. - **Slovjanske sravnenja / comparanda:** ru: стандартный нумерал; uk: стандартний нумерал; pl: numeral standardowy; cs: standardní numerál; bcs: standardni numeral; bg: стандартен нумерал. - **Dokazy / evidence:** OL-MODEL-ARITHMETIC-INTRODUCTION (lines 45-53 and 69-71); RU-MSU-GODEL-LECTURES-2020 (physical page 1 / extracted line 67); CS-CUNI-LOGIC-II-2008 (physical page 1 / extracted lines 27-28); ISV-DICT-LIVE-20260825 (wordList[16187]; dictionary_id=20754; lemma=standardny; gloss=standard); ISV-DICT-LIVE-20260825 (wordList[11898]; dictionary_id=17074; lemma=čislovnik; gloss=numeral); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic, standard flavorization) - **Alternativy / alternatives:** standardny čislovnik: The pinned dictionary row is useful adverse evidence but its Russian, Ukrainian, Polish, Czech, Serbian, and other columns identify the grammatical numeral or number-word sense, which would blur the source's formal term.; standardno čislo: A numeral is a syntactic term denoting a number, not the number itself; this replacement would damage the source's term-value distinction. - **Neizvěstnost / uncertainty:** No direct Ukrainian, Polish, BCS, or Bulgarian printed occurrence of the formal-language noun was pinned for this unit.; The preferred noun numeral is not a headword in the pinned Interslavic dictionary response; it is a reversible edition technical extension. ## OLISV-T0394 · model-theory.standard-part - **English lemma / sense:** standard part of a model — The elements corresponding to the standard natural numbers inside a model of arithmetic. - **Medžuslovjansky:** `standardna čest modela`; lemma `standardna čest modela`; feminine adjective-noun phrase with genitive complement. - **Upotrěbljenje / inflection:** Standardna agrees with feminine čest; modela is genitive singular. The edition's basic reader spelling čest is retained instead of etymological čęsť. - **Kirilična forma:** `стандардна чест модела` - **Argumentacija / rationale:** The phrase directly mirrors the source decomposition and combines dictionary-backed standardny and čęsť under the edition's established basic spelling. It avoids treating the standard part as a separate submodel when only the order reduct is under discussion. - **Uvěrjenost / status:** 0.91 (high); `provisional`; revision `OLISV-T0394-r0001`. - **Slovjanske sravnenja / comparanda:** ru: стандартная часть модели; uk: стандартна частина моделі; pl: standardowa część modelu; cs: standardní část modelu; bcs: standardni dio modela; стандардни део модела; bg: стандартна част на модела. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[12471]; dictionary_id=1731; lemma=čęsť; gloss=part); ISV-DICT-LIVE-20260825 (wordList[16187]; dictionary_id=20754; lemma=standardny); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic and standard flavorization) - **Alternativy / alternatives:** standardno podmnožstvo modela: The source names a structural part, not merely an arbitrary subset, and the longer form obscures its complementarity with the non-standard part.; standardna čęsť modela: Etymological spelling is valid in other registers, but it would break the accepted edition's basic reader surface čest. - **Neizvěstnost / uncertainty:** National mathematical traditions vary between part, copy, and initial-segment terminology depending on which inherited operations are in scope. ## OLISV-T0185 · model-theory.structural-property - **English lemma / sense:** structural property — A property of structures that is invariant under isomorphism; whether such a property is expressible by a sentence or theory is a separate question. - **Medžuslovjansky:** `strukturno svojstvo`; lemma `strukturno svojstvo`; neuter noun phrase. - **Upotrěbljenje / inflection:** The neuter adjective agrees with svojstvo: genitive strukturnogo svojstva; plural strukturna svojstva. - **Kirilična forma:** `структурно својство` - **Argumentacija / rationale:** Strukturno svojstvo is the transparent combination of two directly frozen heads and keeps this model-theoretic sense distinct from OLISV-T0140's generic syntactic-property scope. The source places the term in an expressibility question, so the canon explicitly refuses to equate structurality with first-order expressibility. - **Uvěrjenost / status:** 0.91 (high); `provisional`; revision `OLISV-T0185-r0001`. - **Slovjanske sravnenja / comparanda:** ru: структурное свойство; uk: структурна властивість; pl: własność strukturalna; cs: strukturní vlastnost; bcs: strukturno svojstvo; структурно својство; bg: структурно свойство. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[16425]; dictionary_id=36307; lemma=strukturny; gloss=structural); ISV-DICT-LIVE-20260825 (wordList[3203]; dictionary_id=22019; lemma=svojstvo; gloss=characteristic, property); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** strukturalno svojstvo: The international adjective is intelligible, but the frozen dictionary directly selects strukturny and supplies pan-Slavic cognates; no competing benefit justifies departing from it. - **Neizvěstnost / uncertainty:** The source uses quotation marks and asks which structural properties are sentence-expressible rather than giving a formal definition in this unit.; Isomorphism invariance is the model-theoretic sense boundary; it must not be read as first-order definability. ## OLISV-T0016 · model-theory.structure - **English lemma / sense:** structure — An interpretation domain together with denotations for the non-logical symbols of a first-order language. - **Medžuslovjansky:** `struktura`; lemma `struktura`; feminine noun. - **Upotrěbljenje / inflection:** Feminine noun; genitive singular struktury, nominative plural struktury. Use L-struktura when the signature or language L is explicit. - **Kirilična forma:** `структура` - **Argumentacija / rationale:** Struktura is directly identical or near-identical across all comparison languages and matches Open Logic’s own preferred technical label over its acknowledged synonyms model and interpretation. - **Uvěrjenost / status:** 0.96 (high); `seed_preferred`; revision `OLISV-T0016-r0001`. - **Slovjanske sravnenja / comparanda:** ru: структура; uk: структура; pl: struktura; cs: struktura; bcs: struktura; bg: структура. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[16426]; dictionary_id=16363); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** ustrojstvo: This broader dictionary alternative can mean system, mechanism, or arrangement and is less precise for the model-theoretic object. - **Neizvěstnost / uncertainty:** No specific uncertainty beyond the provisional edition boundary. ## OLISV-T0353 · model-theory.structure-automorphism - **English lemma / sense:** automorphism of a structure — An isomorphism from a first-order structure onto itself; such maps preserve every definable subset. - **Medžuslovjansky:** `avtomorfizm struktury`; lemma `avtomorfizm struktury`; masculine noun with genitive singular complement. - **Upotrěbljenje / inflection:** Use avtomorfizm struktury for the full term and avtomorfizm when the structure is already explicit. Inflect the head regularly; use neizměnny pri avtomorfizmah for invariant under automorphisms. - **Kirilična forma:** `автоморфизм структуры` - **Argumentacija / rationale:** Avtomorfizm retains the shared specialist morph- family while adapting the prefix to standard Interslavic avto-. The same self-isomorphism concept is directly attested in Ukrainian, Polish, Czech, and Croatian academic sources, with several also connecting automorphisms to definability or invariance. The full head avtomorfizm struktury prevents ambiguity outside model theory; the unit may use the short form once the structure is explicit. - **Uvěrjenost / status:** 0.95 (high); `provisional`; revision `OLISV-T0353-r0001`. - **Slovjanske sravnenja / comparanda:** ru: автоморфизм структуры; uk: автоморфізм структури; pl: automorfizm struktury; cs: automorfismus struktury; bcs: automorfizam strukture; аутоморфизам структуре; bg: автоморфизъм на структура. - **Dokazy / evidence:** OL-MODEL-ISOMORPHISM (lines 122-131); UK-KNU-ISOMORPHISM-AUTOMORPHISM-ELEMENTARY-EQUIVALENCE-2022 (physical/printed PDF page 124 and pages 127-128); PL-UW-ISOMORPHISM-AUTOMORPHISM (physical PDF pages 12 and 15-18); CS-CUNI-GEOMETRIC-MODEL-THEORY-SYLLABUS (HTML lines 88-92 and 194-259); HR-ZAGREB-COUNTABLY-MANY-CONSTANTS (additional extract, physical PDF pages 17-18); ISV-DICT-LIVE-20260825 (wordList[9524], wordList[17894]; dictionary_id=19886,36418; neizměnny and neizměnjeny); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; Standard Cyrillic) - **Alternativy / alternatives:** automorfizm struktury: The unadapted international prefix auto- is recognizable but conflicts with the established Interslavic avto- adaptation used for the selected head.; samoizomorfizm struktury: This is descriptively transparent but is not the cross-Slavic specialist head attested by the academic sources and would needlessly separate the edition from standard mathematical usage. - **Neizvěstnost / uncertainty:** No direct official Interslavic dictionary headword for automorphism was found in the pinned response.; The avto- prefix is an edition-level Interslavic normalization from a stable international Slavic family, not a native-language certification. ## OLISV-T0352 · model-theory.structure-isomorphism - **English lemma / sense:** isomorphism of structures — A bijection between two first-order structures that preserves and reflects constants, predicates, and functions of their common language. - **Medžuslovjansky:** `izomorfizm struktur`; lemma `izomorfizm struktur`; masculine noun with genitive plural complement. - **Upotrěbljenje / inflection:** Use izomorfizm for the witnessing map and izomorfne struktury for the relation between structures; inflect izomorfizm regularly while the complement marks the compared domain. - **Kirilična forma:** `изоморфизм структур` - **Argumentacija / rationale:** Izomorfizm is the maximally shared international specialist head across the pinned Ukrainian, Polish, Czech, Montenegrin, and Croatian academic sources. The Interslavic ending -izm matches the already accepted canon family and avoids choosing a single national -ismus or -izam ending. Adding struktur disambiguates the model-theory sense from the already recorded Curry–Howard isomorphism while the running prose may use the shorter head where the domain is explicit. - **Uvěrjenost / status:** 0.97 (high); `provisional`; revision `OLISV-T0352-r0001`. - **Slovjanske sravnenja / comparanda:** ru: изоморфизм структур; uk: ізоморфізм структур; pl: izomorfizm struktur; cs: izomorfismus struktur; bcs: izomorfizam struktura; изоморфизам структура; bg: изоморфизъм на структури. - **Dokazy / evidence:** OL-MODEL-ISOMORPHISM (lines 36-60); UK-KNU-ISOMORPHISM-AUTOMORPHISM-ELEMENTARY-EQUIVALENCE-2022 (physical/printed PDF pages 123-124); CS-CUNI-ISOMORPHISM-ELEMENTARY-EQUIVALENCE (physical PDF pages 24-25, printed pages 96-98); PL-UW-ISOMORPHISM-AUTOMORPHISM (physical PDF page 12 and pages 15-18); HR-ZAGREB-COUNTABLY-MANY-CONSTANTS (additional extract, physical PDF pages 7-9); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; Standard Cyrillic) - **Alternativy / alternatives:** strukturna jednakost: Isomorphism is not literal equality: it permits different underlying objects connected by a structure-preserving bijection.; izomorfnost struktur: The property noun is usable, but the source immediately defines and repeatedly reasons with the witnessing map; izomorfizm keeps the map and relation terminology aligned. - **Neizvěstnost / uncertainty:** No direct official Interslavic dictionary headword for isomorphism was found in the pinned response.; Russian and Bulgarian surfaces are editorial comparanda here; the edition preference rests on the directly pinned Ukrainian, West-Slavic, and South-Slavic academic family. ## OLISV-T0220 · model-theory.structure-size - **English lemma / sense:** size of a structure — The number or cardinality of elements in the domain of a structure, without claiming that the source explicitly uses the technical word cardinality. - **Medžuslovjansky:** `velikost struktury`; lemma `velikost struktury`; feminine abstract noun phrase with genitive singular. - **Upotrěbljenje / inflection:** Feminine head; genitive velikosti struktury. With a named structure use velikost struktury M. - **Kirilična forma:** `великост структуры` - **Argumentacija / rationale:** The source uses informal size and immediately defines it through the number of domain elements. Velikost follows the accepted mathematical-size precedent and remains readable, while the genitive structure phrase avoids importing a cardinality head not required by this unit. - **Uvěrjenost / status:** 0.82 (high); `provisional`; revision `OLISV-T0220-r0001`. - **Slovjanske sravnenja / comparanda:** ru: мощность структуры; размер структуры; uk: потужність структури; розмір структури; pl: moc struktury; liczność struktury; cs: mohutnost struktury; velikost struktury; bcs: kardinalnost strukture; veličina strukture; bg: мощност на структурата; размер на структурата. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[15562]; dictionary_id=5286; lemma=veličina; gloss=size); ISV-DICT-LIVE-20260825 (wordList[16426]; dictionary_id=16363; lemma=struktura; gloss=structure); OL-SIZE-COMPARING-ISV (lines 11-19); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** kardinalnost struktury: The specialist internationalism is precise but absent from this source and lacks direct frozen support here; selecting it would strengthen informal size into an explicit technical label. - **Neizvěstnost / uncertainty:** National terminology divides among power/cardinality, count, and ordinary-size families; the source itself says size rather than cardinality, and the frozen dictionary directly offers veličina rather than preferred velikost. ## OLISV-T0348 · model-theory.substructure - **English lemma / sense:** substructure — A structure for the same language whose domain is included in a larger structure and whose constants, functions, and predicates agree with the larger structure on that included domain. - **Medžuslovjansky:** `podstruktura`; lemma `podstruktura`; feminine noun. - **Upotrěbljenje / inflection:** Use nominative podstruktura, genitive podstruktury, instrumental podstrukturoju, and nominative plural podstruktury. Keep it distinct from podmnožstvo and from redukt. - **Kirilična forma:** `подструктура` - **Argumentacija / rationale:** Podstruktura exactly preserves the formal direction of the Open Logic relation and is immediately recognizable across East, West, and South Slavic terminology. Polish provides an almost line-for-line same-signature definition; Czech, Russian, Ukrainian, and Serbian independently attest the same compound in specialist contexts. The shared Interslavic pod and struktura components make the form morphologically transparent while the formal source keeps it distinct from an arbitrary subset and from a reduct. - **Uvěrjenost / status:** 0.99 (high); `provisional`; revision `OLISV-T0348-r0001`. - **Slovjanske sravnenja / comparanda:** ru: подструктура; uk: підструктура; pl: podstruktura; cs: podstruktura; bcs: podstruktura; подструктура; bg: подструктура. - **Dokazy / evidence:** OL-MODEL-SUBSTRUCTURES (lines 12-44, especially definition defn:substructure); ISV-DICT-LIVE-20260825 (wordList[16426], wordList[17919]; dictionary_id=16363,737; struktura and pod); PL-MIMUW-SUBSTRUCTURES (physical PDF page 4, Definition 16); CS-CUNI-SUBSTRUCTURES (physical PDF page 7, slide 7/15); UK-KPI-ALGEBRAIC-SUBSTRUCTURE (HTML lines 497-499); RU-HSE-MODEL-SUBSTRUCTURE (physical PDF page 2, syllabus items 23 and 34); SR-KG-REDUCT-EXPANSION-2013 (physical PDF page 27, printed page 23); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** substruktura: The Latin international prefix is interpretable, but the directly attested national-language evidence converges more strongly on pod-/pid- and the native prefix is immediately transparent across the target readership.; podmodel: A structure becomes a model only relative to a theory, while the Open Logic definition applies to arbitrary structures for one language; using model would narrow the denotation.; čest struktury: This explanatory phrase is too broad: the source explicitly warns that domain inclusion alone does not make one structure a formal part of another. - **Neizvěstnost / uncertainty:** The complete compound is not a frozen Interslavic dictionary headword; it is a high-confidence specialist formation from two directly attested components.; The Ukrainian witness is from algebraic structures rather than model theory, while Polish, Czech, Russian, and Serbian supply the closer formal domain. ## OLISV-T0399 · model-theory.tennenbaum-theorem - **English lemma / sense:** Tennenbaum's theorem — Up to isomorphism, the standard model of arithmetic is the only computable model of Peano arithmetic; equivalently, no non-standard model of PA has a computable presentation. - **Medžuslovjansky:** `Tennenbaumova teorema`; lemma `Tennenbaumova teorema`; feminine possessive-adjective noun phrase. - **Upotrěbljenje / inflection:** Tennenbaumova agrees with feminine teorema and follows the active Turingova naming precedent. The genitive alternative teorema Tennenbauma remains intelligible but is not the selected head. - **Kirilična forma:** `Тенненбаумова теорема` - **Argumentacija / rationale:** Tennenbaumova teorema combines the active theorem head with the edition's established possessive-adjective name pattern and a direct Slovak specialist occurrence. Russian and Polish directly attest the competing genitive pattern, which remains documented as a readable alternative. The definition includes the essential up-to-isomorphism qualification absent from the source sentence. - **Uvěrjenost / status:** 0.88 (high); `provisional`; revision `OLISV-T0399-r0001`. - **Slovjanske sravnenja / comparanda:** ru: Теорема Тенненбаума; uk: теорема Тенненбаума; pl: Twierdzenie Tennenbauma; cs: Tennenbaumova věta; bcs: Tennenbaumov teorem; Тененбаумова теорема; bg: теорема на Тененбаум. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 42-47 and 117-126; active canon=OLISV-T0273-r0001); ISV-GRAMMAR-ADJ (lines 43-45; active named-person precedent=OLISV-T0024-r0001); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic and standard flavorization) - **Alternativy / alternatives:** teorema Tennenbauma: This direct Russian/Polish-style genitive construction is intelligible and evidence-backed, but the possessive adjective better matches the active Interslavic named-person pattern and direct Slovak usage.; Tennenbaumovo tvrđenje: The generic statement head obscures the established theorem category and weakens continuity with canon T0273. - **Neizvěstnost / uncertainty:** East- and West-Slavic sources divide between genitive and possessive-adjective name constructions; the chosen head is a reversible house preference.; No direct South-Slavic Tennenbaum-theorem occurrence is pinned; South-Slavic comparanda are explicitly componential. ## OLISV-T0064 · model-theory.term-model - **English lemma / sense:** term model — A canonical model whose domain consists of closed terms, or their identity-equivalence classes when identity is present. - **Medžuslovjansky:** `termovy model`; lemma `termovy model`; masculine noun phrase. - **Upotrěbljenje / inflection:** The relational adjective termovy agrees with masculine model; decline model as a masculine noun and the adjective regularly. - **Kirilična forma:** `термовы модел` - **Argumentacija / rationale:** Termovy model keeps the formal-syntax object term distinct from the broader phrase/expression senses while retaining the directly attested and universally recognizable model; the adjective makes the construction legible without English word order. - **Uvěrjenost / status:** 0.64 (medium); `provisional`; revision `OLISV-T0064-r0001`. - **Slovjanske sravnenja / comparanda:** ru: термовая модель; uk: термова модель; pl: model termowy; cs: termový model; bcs: terminski model; bg: термов модел. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[17056]; dictionary_id=2091; lemma=termin; gloss=term (phrase)); ISV-DICT-LIVE-20260825 (wordList[11194]; dictionary_id=19859; lemma=model; gloss=model); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** izrazovy model: Izraz is directly glossed as term, phrase, expression, but that breadth risks confusing a formal term with an arbitrary expression in the construction.; terminovy model: Termin is directly attested for a term as a phrase, but the accepted Open Logic translation already uses term for the formal syntactic category and termin also carries date or deadline senses. - **Neizvěstnost / uncertainty:** The formal logical term root and adjective termovy are edition-level technical choices rather than direct dictionary lemmas; national specialist compounds are recorded as editorial comparanda. ## OLISV-T0076 · model-theory.term-value - **English lemma / sense:** semantic value of a term — The element of a structure's domain denoted by a term under a variable assignment. - **Medžuslovjansky:** `značenje terma`; lemma `značenje terma`; neuter noun phrase. - **Upotrěbljenje / inflection:** Decline značenje as a neuter noun and term as its genitive complement; state dependence on the structure and assignment whenever context does not already fix both. - **Kirilična forma:** `значење терма` - **Argumentacija / rationale:** Značenje terma preserves the East- and South-Slavic meaning or denotation root, matches the accepted translation's exact phrase, and reuses the edition's established term root. The Open Logic source fixes the result as a domain element under a structure and assignment, preventing confusion with informal lexical meaning. - **Uvěrjenost / status:** 0.74 (medium); `provisional`; revision `OLISV-T0076-r0001`. - **Slovjanske sravnenja / comparanda:** ru: значение терма; uk: значення терма; pl: wartość termu; cs: hodnota termu; bcs: vrijednost terma; bg: стойност на терм. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[10877]; dictionary_id=3736; lemma=značeńje; gloss=meaning, significance); ISV-DICT-LIVE-20260825 (wordList[18220]; dictionary_id=2281; lemma=cěnnosť; gloss=value); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** cěnnost terma: Directly supported as a broad mathematical value family, but less clearly signals semantic denotation and diverges from the accepted target phrase; it remains a legitimate documented alternative rather than adverse nonsense.; interpretacija terma: Existing canon reserves interpretacija for assigning denotations to nonlogical symbols; the term value is the resulting domain element, not that assignment process.; vrědnost terma: No registered Interslavic value lemma supports this surface, while vrěd is directly registered with the unrelated meaning ulcer. - **Neizvěstnost / uncertainty:** No registered witness directly attests the complete specialist phrase značenje terma.; Comparison traditions divide between meaning or denotation and value-family terminology. ## OLISV-T0344 · model-theory.textbook - **English lemma / sense:** textbook — A book systematically designed for teaching and learning a subject, here model theory. - **Medžuslovjansky:** `učebnik`; lemma `učebnik`; masculine noun. - **Upotrěbljenje / inflection:** Genitive singular učebnika and nominative plural učebniki; use učebnik teorije modelov. - **Kirilična forma:** `учебник` - **Argumentacija / rationale:** The exact textbook-only head has direct East/South identity and documented West-Slavic counterparts. - **Uvěrjenost / status:** 0.9 (high); `provisional`; revision `OLISV-T0344-r0001`. - **Slovjanske sravnenja / comparanda:** ru: учебник; uk: підручник; pl: podręcznik; cs: učebnice; bcs: udžbenik; уџбеник; bg: учебник. - **Dokazy / evidence:** OL-MODEL-THEORY-PART (line 15); ISV-DICT-LIVE-20260825 (wordList[17102]; dictionary_id=19022; lemma=učebnik; gloss=textbook); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** podrųčnik: The alternative also covers handbook or guide, weakening the source's textbook boundary. - **Neizvěstnost / uncertainty:** West Slavic readers may prefer podręcznik or učebnice-family forms; the edition head remains reversible. ## OLISV-T0019 · model-theory.theory - **English lemma / sense:** theory — A set of sentences closed under, or considered with respect to, logical consequence. - **Medžuslovjansky:** `teorija`; lemma `teorija`; feminine noun. - **Upotrěbljenje / inflection:** Feminine noun; genitive singular teorije, nominative plural teorije. Use teorija struktury M and model teorije T with genitive complements. - **Kirilična forma:** `теорија` - **Argumentacija / rationale:** Teorija is directly uniform across every comparison language and established throughout the inherited mathematical corpus; Open Logic supplies the specialist semantic boundary. - **Uvěrjenost / status:** 0.99 (high); `seed_preferred`; revision `OLISV-T0019-r0001`. - **Slovjanske sravnenja / comparanda:** ru: теория; uk: теорія; pl: teoria; cs: teorie; bcs: teorija; bg: теория. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[17168]; dictionary_id=4739); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** učenje: Učenje is closer to a doctrine or body of teaching and is not the stable formal-mathematical internationalism. - **Neizvěstnost / uncertainty:** No specific uncertainty beyond the provisional edition boundary. ## OLISV-T0383 · model-theory.theory-of-structure - **English lemma / sense:** theory of a structure; true arithmetic theory TA — The set of all first-order sentences in the structure's language that are true in that structure; for the standard natural-number structure this is complete true arithmetic TA, not Q or PA. - **Medžuslovjansky:** `teorija struktury`; lemma `teorija struktury`; feminine noun with genitive complement. - **Upotrěbljenje / inflection:** Feminine teorija plus genitive singular struktury. In this unit teorija struktury N denotes TA; optional istinna aritmetika is an explanatory alias, not the preferred indexed head. - **Kirilična forma:** `теорија структуры` - **Argumentacija / rationale:** Teorija struktury is a transparent composition of two established canon heads and matches direct Polish and Czech specialist usage. Keeping the explicit structure complement prevents TA from being confused with Robinson or Peano arithmetic and states exactly why the theory is complete. - **Uvěrjenost / status:** 0.99 (high); `provisional`; revision `OLISV-T0383-r0001`. - **Slovjanske sravnenja / comparanda:** ru: теория структуры; uk: теорія структури; pl: teoria struktury; cs: teorie struktury; bcs: teorija strukture; istinita aritmetika TA; bg: теория на структурата. - **Dokazy / evidence:** OL-MODEL-THEORY-M (lines 13-20); OL-MODEL-ARITHMETIC-NONSTANDARD-MODELS (lines 79-98); ISV-DICT-LIVE-20260824 (wordList[17168]; dictionary_id=4739; lemma=teorija); ISV-DICT-LIVE-20260824 (wordList[16426]; dictionary_id=16363; lemma=struktura); PL-UW-MATHEMATICAL-LOGIC-2014-15 (printed page 15 / extracted lines 745-751); HR-ZAGREB-GODEL-INCOMPLETENESS-2011 (printed page 14 / extracted lines 675-681); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic, standard flavorization) - **Alternativy / alternatives:** polna teorija aritmetiky: Completeness alone does not identify the intended complete theory; many complete extensions are possible.; istinna aritmetika: Useful as an explanatory alias for TA, but less explicit than the source's general theory-of-a-structure construction. - **Neizvěstnost / uncertainty:** The standalone alias istinna aritmetika remains provisional and is not used as the preferred index term. ## OLISV-T0206 · number-theory.divisibility - **English lemma / sense:** divisibility; divides; multiple of — The integer or natural-number relation in which n divides m exactly when m equals kn for some integer or natural number k; equivalently m is a multiple of n. - **Medžuslovjansky:** `dělimost bez ostatka`; lemma `dělimost bez ostatka`; feminine noun phrase with controlled predicates. - **Upotrěbljenje / inflection:** Feminine head; genitive dělimosti bez ostatka. Use n děli m bez ostatka and, where the direction needs emphasis, m jest kratno n. - **Kirilična forma:** `дєлимост без остатка` - **Argumentacija / rationale:** The descriptive head and predicate are already established in accepted mathematical prose and avoid mistranslating English evenly as uniformly. The multiple-of wording remains an indexed controlled alias rather than a redundant second relation. - **Uvěrjenost / status:** 0.91 (high); `provisional`; revision `OLISV-T0206-r0001`. - **Slovjanske sravnenja / comparanda:** ru: делимость; n делит m; m кратно n; uk: подільність; n ділить m; m кратне n; pl: podzielność; n dzieli m; m jest wielokrotnością n; cs: dělitelnost; n dělí m; m je násobkem n; bcs: djeljivost; n dijeli m; m je višekratnik n; дељивост; bg: делимост; n дели m; m е кратно на n. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[15251]; dictionary_id=1754; lemma=děliti; gloss=divide); ISV-DICT-LIVE-20260825 (wordList[14356]; dictionary_id=1918; lemma=ostatȯk; gloss=remainder); OL-REL-ORDERS-ISV (lines 63-69); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** ravnoměrna dělimost: Here English evenly means without remainder, not uniformity. The calque would misstate the arithmetic condition and obscure the accepted exact-division wording. - **Neizvěstnost / uncertainty:** No frozen dictionary row directly certifies mathematical kratno; the multiple-of alias is retained at lower confidence than the canonical divisibility head. ## OLISV-T0207 · number-theory.prime-number - **English lemma / sense:** prime number — A natural number greater than one whose positive divisors are exactly one and itself; the current source's informal gloss omits the greater-than-one condition and therefore wrongly admits 1. - **Medžuslovjansky:** `prosto čislo`; lemma `prosto čislo`; neuter noun phrase. - **Upotrěbljenje / inflection:** The adjective agrees with čislo: genitive prostogo čisla and plural prosta čisla. - **Kirilična forma:** `просто число` - **Argumentacija / rationale:** Prosto čislo follows the dominant East, South, and Bulgarian specialist family and remains immediately analyzable. The comparison table explicitly preserves the divergent Polish first-number and Czech compound traditions. - **Uvěrjenost / status:** 0.88 (high); `provisional`; revision `OLISV-T0207-r0001`. - **Slovjanske sravnenja / comparanda:** ru: простое число; uk: просте число; pl: liczba pierwsza; cs: prvočíslo; bcs: prost broj; прост број; bg: просто число. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[15474]; dictionary_id=2334; lemma=prosty; gloss=simple, easy, plain); ISV-DICT-LIVE-20260825 (wordList[11893]; dictionary_id=17215; lemma=čislo; gloss=number); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** prvotno čislo: The proposed primary or original calque suggests order or origin rather than primality and is less recognizable than the established prost- specialist family. - **Neizvěstnost / uncertainty:** The prosty dictionary row attests ordinary simple or plain senses, not the mathematical homonym.; The source gloss omits n > 1 and therefore admits 1; the translation preserves rather than silently repairs that defect. ## OLISV-T0274 · number.composite - **English lemma / sense:** composite number — A natural number that is not prime and has a nontrivial factorization. - **Medžuslovjansky:** `složeno čislo`; lemma `složeno čislo`; neuter adjective-noun phrase. - **Upotrěbljenje / inflection:** Neuter čislo; plural složene čisla, genitive složenogo čisla. - **Kirilična forma:** `сложено число` - **Argumentacija / rationale:** Složeno čislo combines direct dictionary components and preserves the standard Slavic arithmetic contrast with prosto čislo. - **Uvěrjenost / status:** 0.98 (high); `provisional`; revision `OLISV-T0274-r0001`. - **Slovjanske sravnenja / comparanda:** ru: составное число; uk: складене число; pl: liczba złożona; cs: složené číslo; bcs: složen broj; сложен број; bg: съставно число. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 19-26); ISV-DICT-LIVE-20260825 (dictionary_id=6145; lemma=složeny; gloss=complex, complicated, composite, compound); ISV-DICT-LIVE-20260825 (dictionary_id=17215; lemma=čislo; gloss=number); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** kompozitno čislo: The international adjective is less immediately transparent than the direct pan-Slavic složen- family. - **Neizvěstnost / uncertainty:** National languages divide between složen- and sostavn-/skladen- roots; the selected form is the edition compromise. ## OLISV-T0160 · number.integer - **English lemma / sense:** integer — A positive or negative whole number, or zero; here used as an alternative domain for a structure for the language of arithmetic. - **Medžuslovjansky:** `cělo čislo`; lemma `cělo čislo`; neuter noun phrase. - **Upotrěbljenje / inflection:** Genitive singular cělogo čisla in grammatical prose; plural cěla čisla. The canonical head is the complete direct dictionary phrase. - **Kirilična forma:** `цєло число` - **Argumentacija / rationale:** The frozen dictionary directly supplies the complete mathematical phrase and its six-language comparison columns; the source fixes the model-theoretic use as the domain of an arithmetic structure. - **Uvěrjenost / status:** 0.97 (high); `provisional`; revision `OLISV-T0160-r0001`. - **Slovjanske sravnenja / comparanda:** ru: целое число; uk: ціле число; pl: liczba całkowita; cs: celé číslo; bcs: cijeli broj; цео број; bg: цяло число. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-DICT-LIVE-20260825 (wordList[9375]; dictionary_id=36585); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** cělostno čislo: This unattested calque is unnecessary beside the direct complete dictionary lemma. - **Neizvěstnost / uncertainty:** Croatian and Serbian use the number rather than numeral head, as recorded in the direct dictionary row. ## OLISV-T0275 · number.irrational - **English lemma / sense:** irrational number — A real number that is not rational. - **Medžuslovjansky:** `iracionaľno čislo`; lemma `iracionaľno čislo`; neuter adjective-noun phrase. - **Upotrěbljenje / inflection:** Neuter čislo; plural iracionaľne čisla, genitive iracionaľnogo čisla. - **Kirilična forma:** `ирационално число` - **Argumentacija / rationale:** The accepted real-number unit already uses the positive iracional- family, and the dictionary's neracionaľny row confirms the specialist sense and soft-l spelling. Iracionaľno avoids reading the initial ne- as a freely scoped negation in dense formulas. - **Uvěrjenost / status:** 0.91 (high); `provisional`; revision `OLISV-T0275-r0001`. - **Slovjanske sravnenja / comparanda:** ru: иррациональное число; uk: ірраціональне число; pl: liczba niewymierna; cs: iracionální číslo; bcs: iracionalan broj; ирационалан број; bg: ирационално число. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 37-72); OL-SFR-ARITHMETIZATION-REALS-ISV (line 22: iracionalne čisla ... realne čisla, ktore ne sųt racionalne); ISV-DICT-LIVE-20260825 (dictionary_id=19902; lemma=neracionaľny; gloss=irrational); ISV-DICT-LIVE-20260825 (dictionary_id=17215; lemma=čislo; gloss=number); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** neracionaľno čislo: Directly listed, but the negative form is less stable across the existing edition than the accepted positive international family. - **Neizvěstnost / uncertainty:** The accepted precedent spells iracionalne without the soft-l mark; the OLP0179 form regularizes it to the pinned adjective family. ## OLISV-T0184 · number.natural - **English lemma / sense:** natural number — A member of the standard set of natural numbers denoted by Nat; distinct from a numeral, an arbitrary integer, or the cardinality of a collection. - **Medžuslovjansky:** `prirodno čislo`; lemma `prirodno čislo`; neuter noun phrase. - **Upotrěbljenje / inflection:** The neuter adjective agrees with čislo: genitive prirodnogo čisla; plural prirodna čisla. - **Kirilična forma:** `природно число` - **Argumentacija / rationale:** Prirodno čislo combines two directly frozen heads and gives especially strong South-Slavic and Czech-root transparency while remaining reconstructible elsewhere. The source occurrence explicitly binds the phrase to the carrier Nat. Its surrounding non-expressibility sentence is logically defective, but that defect does not alter the lexical identity of the numbers named. - **Uvěrjenost / status:** 0.77 (medium); `provisional`; revision `OLISV-T0184-r0001`. - **Slovjanske sravnenja / comparanda:** ru: натуральное число; uk: натуральне число; pl: liczba naturalna; cs: přirozené číslo; bcs: prirodan broj; природан број; bg: естествено число. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[11548]; dictionary_id=1215; lemma=prirodny; gloss=natural); ISV-DICT-LIVE-20260825 (wordList[11893]; dictionary_id=17215; lemma=čislo; gloss=number); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** naturalno čislo: The international adjective is highly recognizable in East and West Slavic mathematical usage, but prirodny is the selected directly frozen bridge to Czech přirozený and South-Slavic prirodan while still listing naturalny as an explicit reversible alternative. - **Neizvěstnost / uncertainty:** No frozen dictionary row directly attests the complete Interslavic mathematical compound.; The source's surrounding only-if/contains-only claim is logically defective and is preserved as adverse evidence rather than used as semantic proof. ## OLISV-T0253 · number.rational - **English lemma / sense:** rational number — A number representable as a quotient of integers with non-zero denominator. - **Medžuslovjansky:** `racionaľno čislo`; lemma `racionaľno čislo`; neuter adjective-noun phrase. - **Upotrěbljenje / inflection:** Plural racionaľna čisla; genitive racionaľnogo čisla. Use the spelling racionaľny in prose adjectives. - **Kirilična forma:** `рационално число` - **Argumentacija / rationale:** Both components are directly pinned and the source uses the phrase in its standard mathematical sense. The target surface racionalna čisla is the plural inflection of this head. - **Uvěrjenost / status:** 0.97 (high); `provisional`; revision `OLISV-T0253-r0002`. - **Slovjanske sravnenja / comparanda:** ru: рациональное число; uk: раціональне число; pl: liczba wymierna; cs: racionální číslo; bcs: racionalni broj; рационални број; bg: рационално число. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (dictionary_id=16337; lemma=racionaľny; gloss=rational); ISV-DICT-LIVE-20260825 (dictionary_id=17215; lemma=čislo; gloss=number); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** lomno čislo: Can be read as any fractional-looking number and is not the standard field-theoretic class name.; racionaľnost: Names the property rather than an individual number. - **Neizvěstnost / uncertainty:** Some national languages use a distinct 'quotient/fraction' root; the international adjective remains highly legible.; The r0001 record remains preserved as adverse provenance for the target/source locator mismatch. ## OLISV-T0254 · number.real - **English lemma / sense:** real number — An element of the complete ordered field used as the real-number structure. - **Medžuslovjansky:** `reaľno čislo`; lemma `reaľno čislo`; neuter adjective-noun phrase. - **Upotrěbljenje / inflection:** Plural reaľna čisla; genitive reaľnogo čisla. Keep real as the adjective root distinct from reality nouns. - **Kirilična forma:** `реално число` - **Argumentacija / rationale:** Reaľny is directly present in the dictionary and is the accessible pan-Slavic choice for the source's real-number phrase. The canon records the complete ordered-field qualification separately. - **Uvěrjenost / status:** 0.95 (high); `provisional`; revision `OLISV-T0254-r0002`. - **Slovjanske sravnenja / comparanda:** ru: вещественное число; uk: дійсне число; pl: liczba rzeczywista; cs: reálné číslo; bcs: realni broj; реални број; bg: реално число. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (dictionary_id=2216; lemma=reaľny; gloss=real, actual (real)); ISV-DICT-LIVE-20260825 (dictionary_id=17215; lemma=čislo; gloss=number); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** stvаŕno čislo: Stvaŕny emphasizes actual/existing and is not the standard mathematical class name.; čislo realnosti: A literal genitive construction is opaque and risks a philosophical rather than numerical reading. - **Neizvěstnost / uncertainty:** East-Slavic mathematical usage often prefers the 'material/actual' root; the selected international form remains documented in the dictionary.; The r0001 record remains preserved as adverse provenance for the target/source locator mismatch. ## OLISV-T0282 · philosophy.constructivism - **English lemma / sense:** constructivism — The mathematical-philosophical programme associated here with Bishop and concrete constructive proof. - **Medžuslovjansky:** `konstruktivizm`; lemma `konstruktivizm`; masculine noun. - **Upotrěbljenje / inflection:** Masculine konstruktivizm; genitive konstruktivizma. - **Kirilična forma:** `конструктивизм` - **Argumentacija / rationale:** Konstruktivizm transparently derives from the direct construction family and names the source's Bishop-associated programme without collapsing it into intuitionism. - **Uvěrjenost / status:** 0.9 (high); `provisional`; revision `OLISV-T0282-r0001`. - **Slovjanske sravnenja / comparanda:** ru: конструктивизм; uk: конструктивізм; pl: konstruktywizm; cs: konstruktivismus; bcs: konstruktivizam; конструктивизам; bg: конструктивизъм. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 81-95); ISV-DICT-LIVE-20260825 (dictionary_id=4873; lemma=konstrukcija; gloss=construction); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** konstruktivna filosofija: The paraphrase is broader than the named mathematical programme and loses its conventional label. - **Neizvěstnost / uncertainty:** The dictionary supplies the root rather than the complete philosophical derivative. ## OLISV-T0281 · philosophy.intuitionism - **English lemma / sense:** intuitionism — The philosophical position associated with Brouwer that motivates intuitionistic mathematical reasoning. - **Medžuslovjansky:** `intuicionizm`; lemma `intuicionizm`; masculine noun. - **Upotrěbljenje / inflection:** Masculine intuicionizm; genitive intuicionizma. - **Kirilična forma:** `интуиционизм` - **Argumentacija / rationale:** Intuicionizm is a regular international derivative of the direct intuicija root and keeps the philosophical school distinct from the formal logic T0269. - **Uvěrjenost / status:** 0.9 (high); `provisional`; revision `OLISV-T0281-r0001`. - **Slovjanske sravnenja / comparanda:** ru: интуиционизм; uk: інтуїціонізм; pl: intuicjonizm; cs: intuicionismus; bcs: intuicionizam; интуиционизам; bg: интуиционизъм. - **Dokazy / evidence:** OL-FOL-BEYOND-INTUITIONISTIC-LOGIC (lines 81-95 and 128-133); ISV-DICT-LIVE-20260825 (dictionary_id=6159; lemma=intuicija; gloss=intuition); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** filosofija intuicije: A descriptive phrase does not identify the named historical school and may suggest psychology. - **Neizvěstnost / uncertainty:** The complete derivative is not a direct dictionary row; its school sense is fixed by the source's Brouwer attribution. ## OLISV-T0226 · philosophy.logicism - **English lemma / sense:** logicism — The philosophical and foundational program, begun here with Frege and continued by Russell and Whitehead, of developing mathematics on the basis of logic. - **Medžuslovjansky:** `logicizm`; lemma `logicizm`; masculine noun. - **Upotrěbljenje / inflection:** Genitive logicizma; adjective logicističny. Use for the historical program, not for any merely logical style of argument. - **Kirilična forma:** `логицизм` - **Argumentacija / rationale:** The international -ism name is the concise, pan-Slavically recognizable label for the specific Frege-Russell-Whitehead program described by the source. - **Uvěrjenost / status:** 0.78 (medium); `provisional`; revision `OLISV-T0226-r0001`. - **Slovjanske sravnenja / comparanda:** ru: логицизм; uk: логіцизм; pl: logicyzm; cs: logicismus; bcs: logicizam; логицизам; bg: логицизъм. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[10431]; dictionary_id=8933; lemma=logika; gloss=logic); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** logičny redukcionizm: This explanatory phrase is not the historical movement's name and would overselect one interpretation of the program. - **Neizvěstnost / uncertainty:** The frozen dictionary lacks a direct logicizm row; the selected head is a source-bounded editorial internationalism. ## OLISV-T0179 · proof.axiom-independence - **English lemma / sense:** independence of axioms — The property that no axiom in a system is semantically entailed by the remaining axioms; non-entailment may be witnessed by a model of the others plus its negation. - **Medžuslovjansky:** `nezavisnost aksiom`; lemma `nezavisnost aksiom`; feminine noun phrase. - **Upotrěbljenje / inflection:** Nezavisnost is a feminine consonant noun; use genitive nezavisnosti. Aksiom is genitive plural in the fixed phrase. - **Kirilična forma:** `независност аксиом` - **Argumentacija / rationale:** Nezavisnost aksiom combines two directly frozen and broadly recognizable components, while Open Logic supplies the exact model-theoretic witness condition. It also avoids confusing independence with the stronger political sense sometimes carried by nezaležnost. - **Uvěrjenost / status:** 0.88 (high); `provisional`; revision `OLISV-T0179-r0001`. - **Slovjanske sravnenja / comparanda:** ru: независимость аксиом; uk: незалежність аксіом; pl: niezależność aksjomatów; cs: nezávislost axiomů; bcs: nezavisnost aksioma; bg: независимост на аксиомите. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[9140,9143]; dictionary_id=17957,17958; lemma=nezavisnosť,nezavisny; gloss=independence,independent); ISV-DICT-LIVE-20260825 (wordList[1498]; dictionary_id=24180; lemma=aksioma; gloss=axiom); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** nezaležnost aksiom: Nezaležnost is a listed synonym and is strong in Ukrainian and Polish, but nezavisnost aligns directly with Russian, Czech/Slovak cognates, BCS, Macedonian, and Bulgarian while avoiding political-independence overtones. - **Neizvěstnost / uncertainty:** The complete technical compound is assembled editorially even though both components are directly attested. ## OLISV-T0059 · proof.consistency - **English lemma / sense:** consistency — The property of a set of formulas for which no closed proof of contradiction exists under the selected proof system. - **Medžuslovjansky:** `nesprotivnost`; lemma `nesprotivnost`; noun. - **Upotrěbljenje / inflection:** Feminine abstract noun; protivny and nesprotivny are the corresponding negative and positive adjectives in this edition. - **Kirilična forma:** `неспротивност` - **Argumentacija / rationale:** Nesprotivnost exposes the absence of contradiction directly and bridges the widespread Slavic protiv/sprzecz/spor families without relying on the less transparent international loan konsistentnost. - **Uvěrjenost / status:** 0.7 (medium); `provisional`; revision `OLISV-T0059-r0001`. - **Slovjanske sravnenja / comparanda:** ru: непротиворечивость; uk: несуперечливість; pl: niesprzeczność; cs: bezespornost; bcs: neprotivrečnost; bg: непротиворечивост. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** konsistentnost: The international loan is concise but less immediately parsable to readers without English or specialist Latin-derived vocabulary. - **Neizvěstnost / uncertainty:** Czech and Ukrainian specialist traditions use different lexical roots, and the compact Interslavic form is an edition-level compromise rather than a certified native term. ## OLISV-T0374 · proof.consistency-statement - **English lemma / sense:** consistency statement — A formal sentence expressing that the selected theory has no coded derivation of contradiction, here the sentence Con(PA). - **Medžuslovjansky:** `tvrdženje o nesprotivnosti`; lemma `tvrdženje o nesprotivnosti`; neuter noun phrase with prepositional complement. - **Upotrěbljenje / inflection:** Neuter tvrdženje plus locative o nesprotivnosti; genitive tvrdženja o nesprotivnosti. Use the shorter nesprotivnost only for the property, not the sentence expressing it. - **Kirilična forma:** `тврджење о неспротивности` - **Argumentacija / rationale:** Tvrdženje o nesprotivnosti composes the established canon property nesprotivnost (OLISV-T0059) with the established truth-apt statement head tvrdženje. The expanded phrase prevents a categorical error: the source is discussing a sentence that expresses consistency, not consistency itself. - **Uvěrjenost / status:** 0.86 (high); `provisional`; revision `OLISV-T0374-r0001`. - **Slovjanske sravnenja / comparanda:** ru: утверждение о непротиворечивости; uk: твердження про несуперечливість; pl: twierdzenie o niesprzeczności; cs: tvrzení o bezespornosti; bcs: tvrdnja o neprotivrečnosti; тврдња о непротивречности; bg: твърдение за непротиворечивост. - **Dokazy / evidence:** OL-MODEL-ARITHMETIC-INTRODUCTION (lines 55-64); ISV-DICT-LIVE-20260825 (wordList[16219]; dictionary_id=1087; lemma=tvŕđeńje; gloss=statement, claim, assertion); RU-MSU-GODEL-LECTURES-2020 (physical page 8 / extracted lines 395-402); CS-CUNI-LOGIC-II-2008 (physical pages 1-2 / extracted lines 38-51); UK-KNU-LOGIC-FOUNDATIONS-2020 (physical page 92 / extracted lines 3929-4003); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic, standard flavorization) - **Alternativy / alternatives:** nesprotivnost: This is the established property head but is too compressed when the grammar requires the formal sentence Con(PA) as an object that can be proved, negated, or satisfied.; izrečenje nesprotivnosti: It is structurally possible, but tvrdženje is the established truth-apt claim head and the prepositional complement makes the semantic relation clearer. - **Neizvěstnost / uncertainty:** The exact complete phrase is a project-house composition rather than a standalone dictionary headword.; Polish, BCS, and Bulgarian full national phrases are transparent editorial comparanda in this packet. ## OLISV-T0176 · proof.contraposition - **English lemma / sense:** contraposition — The transformation or proof method that replaces an implication from A to B by the equivalent implication from not-B to not-A; in the source it proves the reverse direction through its contrapositive. - **Medžuslovjansky:** `kontrapozicija`; lemma `kontrapozicija`; feminine abstract noun. - **Upotrěbljenje / inflection:** Instrumental kontrapozicijoju; genitive kontrapozicije. Use for the implication transformation or proof method, not for dokaz od protivnogo and not for the converse implication. - **Kirilična forma:** `контрапозиција` - **Argumentacija / rationale:** Kontrapozicija preserves the highly convergent international logical term across East, West, and South Slavic comparison languages. Its dedicated sense note distinguishes the implication transformation from both the converse and proof by contradiction, a distinction made locally by the two adjacent proof strategies in Open Logic. - **Uvěrjenost / status:** 0.9 (high); `provisional`; revision `OLISV-T0176-r0001`. - **Slovjanske sravnenja / comparanda:** ru: контрапозиция; uk: контрапозиція; pl: kontrapozycja; cs: kontrapozice; bcs: kontrapozicija; контрапозиција; bg: контрапозиция. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[13187]; dictionary_id=1225; lemma=pozicija; gloss=position); ISV-DICT-LIVE-20260825 (wordList[4132]; dictionary_id=19795; lemma=kontrakcija; gloss=contraction); ISV-DICT-LIVE-20260825 (wordList[4136]; dictionary_id=4388; lemma=protivny; gloss=contrary); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** dokaz od protivnogo: Proof by contradiction assumes the negation of the desired result and derives inconsistency; it is explicitly a different method in the following proof and cannot replace contraposition.; obratno tvrđenje: The converse swaps antecedent and consequent without negating them and is not logically equivalent in general; it names a different transformation.; kontrapozitiv: This can name the resulting contrapositive conditional, whereas the source sentence and selected head denote the transformation or proof method. - **Neizvěstnost / uncertainty:** No frozen Interslavic dictionary row directly attests the complete formal-logic lemma.; Some pedagogical traditions use the related noun for the resulting conditional rather than the transformation; the canon sense is explicitly method-first. ## OLISV-T0015 · proof.deduction - **English lemma / sense:** deduction — A rule-governed inference process, especially the natural-deduction proof system. - **Medžuslovjansky:** `dedukcija`; lemma `dedukcija`; feminine noun. - **Upotrěbljenje / inflection:** Feminine noun; genitive singular dedukcije. Use prirodna dedukcija for the proof system and deduktivny only for the corresponding adjective. - **Kirilična forma:** `дедукција` - **Argumentacija / rationale:** The international term is directly and uniformly attested, and it forms an unambiguous collocation with prirodna for Open Logic’s proof system. - **Uvěrjenost / status:** 0.96 (high); `seed_preferred`; revision `OLISV-T0015-r0001`. - **Slovjanske sravnenja / comparanda:** ru: дедукция; uk: дедукція; pl: dedukcja; cs: dedukce; bcs: dedukcija; bg: дедукция. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[4819]; dictionary_id=25162); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** izvod: Izvod is directly listed for conclusion, deduction, and inference, but it denotes an inference result more readily than the named proof system. - **Neizvěstnost / uncertainty:** No specific uncertainty beyond the provisional edition boundary. ## OLISV-T0316 · proof.deductive-system - **English lemma / sense:** deductive system — A formal system of rules used to derive conclusions and assessed in the source for completeness relative to a semantics. - **Medžuslovjansky:** `deduktivny sistem`; lemma `deduktivny sistem`; masculine adjective-noun phrase. - **Upotrěbljenje / inflection:** Masculine sistem; genitive deduktivnogo sistema and plural deduktivne sistemy. - **Kirilična forma:** `дедуктивны систем` - **Argumentacija / rationale:** Deduktivny sistem combines the directly attested adjective with the edition's established masculine sistem head. It is kept distinct from the broader sistem izvodženja: the source first names a deductive system and then separately marks the derivation system whose completeness matters. - **Uvěrjenost / status:** 0.91 (high); `provisional`; revision `OLISV-T0316-r0001`. - **Slovjanske sravnenja / comparanda:** ru: дедуктивная система; uk: дедуктивна система; pl: system dedukcyjny; cs: deduktivní systém; bcs: deduktivni sistem; дедуктивни систем; bg: дедуктивна система. - **Dokazy / evidence:** OL-FOL-BEYOND-OTHER-LOGICS (lines 14-18); ISV-DICT-LIVE-20260825 (dictionary_id=25163; lemma=deduktivny; gloss=deductive); ISV-DICT-LIVE-20260825 (dictionary_id=1317; lemma=sistema; gloss=system); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** sistem izvodženja: That established broader term correctly translates derivation system later in the sentence, but collapsing the two source labels would erase the deliberate lexical distinction. - **Neizvěstnost / uncertainty:** The frozen dictionary lists feminine sistema while the edition consistently uses masculine sistem; the normalization is explicit rather than presented as a dictionary quotation. ## OLISV-T0325 · proof.defeasible-inference - **English lemma / sense:** defeasible inference — An inference that is licensed as reasonable in the current information state but can later be overturned. - **Medžuslovjansky:** `odzyvatelny vyvod`; lemma `odzyvatelny vyvod`; masculine adjective-noun phrase. - **Upotrěbljenje / inflection:** Masculine vyvod; genitive odzyvateljnogo vyvoda and plural odzyvatelne vyvody. - **Kirilična forma:** `одзывателны вывод` - **Argumentacija / rationale:** Odzyvatelny vyvod reuses the edition's established vyvod head and directly encodes the source's ability to withdraw it. The quoted reasonable qualifier remains in running prose and is not mistaken for the technical name itself. - **Uvěrjenost / status:** 0.8 (high); `provisional`; revision `OLISV-T0325-r0001`. - **Slovjanske sravnenja / comparanda:** ru: отменяемый вывод; uk: спростовний висновок; pl: wniosek podważalny; cs: zrušitelný závěr; bcs: opoziv zaključak; опозив закључак; bg: отменим извод. - **Dokazy / evidence:** OL-FOL-BEYOND-OTHER-LOGICS (lines 26-28); ISV-DICT-LIVE-20260825 (dictionary_id=32459; lemma=odzvati; gloss=withdraw, recall); ISV-DICT-LIVE-20260825 (dictionary_id=22276; lemma=izvod; gloss=conclusion, deduction, inference); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** razumny vyvod: The source places reasonable in quotation marks as an informal gloss; it does not express the crucial possibility of later withdrawal. - **Neizvěstnost / uncertainty:** The frozen dictionary head is izvod while the edition already normalizes the inferential surface to vyvod; that lineage remains explicit. ## OLISV-T0324 · proof.defeasible-reasoning - **English lemma / sense:** defeasible reasoning — Reasoning whose apparently reasonable conclusions may later be withdrawn when relevant new information is supplied. - **Medžuslovjansky:** `odzyvatelno razsuđanje`; lemma `odzyvatelno razsuđanje`; neuter adjective-verbal-noun phrase. - **Upotrěbljenje / inflection:** Neuter razsuđanje; genitive odzyvateljnogo razsuđanja and contextual genitive plural odzyvatelnyh form razsuđanja. - **Kirilična forma:** `одзывателно разсуджање` - **Argumentacija / rationale:** Odzyvatelno razsuđanje makes reversibility under new information explicit by combining the withdrawal family with the edition's established razsuđanje head. It avoids importing the misleading everyday sense of weak or easily defeated thought. - **Uvěrjenost / status:** 0.78 (medium); `provisional`; revision `OLISV-T0324-r0001`. - **Slovjanske sravnenja / comparanda:** ru: отменяемое рассуждение; uk: спростовне міркування; pl: rozumowanie podważalne; cs: zrušitelné usuzování; bcs: opozivo rasuđivanje; опозиво расуђивање; bg: отменимо разсъждение. - **Dokazy / evidence:** OL-FOL-BEYOND-OTHER-LOGICS (lines 25-28); ISV-DICT-LIVE-20260825 (dictionary_id=32460; lemma=odzyvati; gloss=withdraw, recall); ISV-DICT-LIVE-20260825 (dictionary_id=34021; lemma=råzsųđati; gloss=reason); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** odrěčimo razsuđanje: Odrěkti can suggest verbally denying a claim; the source requires the technical ability to withdraw an inference after information changes. - **Neizvěstnost / uncertainty:** The complete adjective-noun compound is editorial, and defeasible has no single uniformly adopted Slavic calque. ## OLISV-T0079 · proof.derivability - **English lemma / sense:** derivability — The syntactic relation holding when a proof system licenses a derivation of a conclusion from premises. - **Medžuslovjansky:** `izvodivost`; lemma `izvodivost`; feminine abstract noun. - **Upotrěbljenje / inflection:** Use odnošenje izvodivosti for the relation and distinguish it from semantic slědovanje. - **Kirilična forma:** `изводивост` - **Argumentacija / rationale:** A regular abstraction from the selected derive family keeps the syntactic relation visibly distinct from semantic entailment. - **Uvěrjenost / status:** 0.62 (medium); `provisional`; revision `OLISV-T0079-r0001`. - **Slovjanske sravnenja / comparanda:** ru: выводимость; uk: вивідність; виводимість; pl: wyprowadzalność; cs: odvoditelnost; bcs: izvodivost; bg: изводимост. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[5013-5015]; dictionary_id=17598,36763,36764); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** dokazivost: Provability can suggest theoremhood rather than the explicitly parameterized relation.; derivabilnost: The international loan is not directly listed and is less parsable without specialist vocabulary. - **Neizvěstnost / uncertainty:** National proof-theory terminology varies between derivability and provability families. ## OLISV-T0077 · proof.derivation - **English lemma / sense:** derivation — A finite formal object licensed by a proof system and establishing a derivability claim. - **Medžuslovjansky:** `izvodženje`; lemma `izvodženje`; neuter verbal noun. - **Upotrěbljenje / inflection:** Genitive singular izvodženja; reserve dokaz for a completed proof and izvodženje for the formal construction or process. - **Kirilična forma:** `изводжење` - **Argumentacija / rationale:** Izvodženje is the standard-Latin normalization of the directly listed derivation noun izvođeńje; it spans Czech and South-Slavic odvoz-/izvod- traditions while remaining recognizable beside East-Slavic vyvod, and Open Logic excludes ordinary origin and morphology senses. - **Uvěrjenost / status:** 0.72 (medium); `provisional`; revision `OLISV-T0077-r0001`. - **Slovjanske sravnenja / comparanda:** ru: вывод; выведение; uk: виведення; деривація; pl: wyprowadzenie; derywacja; cs: odvození; bcs: izvođenje; bg: извод; извеждане. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[5013]; dictionary_id=17598); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** dedukcija: Deduction is a broader method and not specifically the finite derivation object.; dokaz: Proof or evidence is broader than the licensed construction described here. - **Neizvěstnost / uncertainty:** The direct dictionary row uses an etymological/extended surface and is polysemous across derivation, origin, and morphology.; East-Slavic readers may expect a vyvod surface. ## OLISV-T0078 · proof.derivation-system - **English lemma / sense:** derivation system — A formal system whose licensed finite derivations determine a syntactic derivability relation. - **Medžuslovjansky:** `sistem izvodženja`; lemma `sistem izvodženja`; masculine noun phrase. - **Upotrěbljenje / inflection:** Genitive singular sistema izvodženja; use korektny and polny for sound and complete systems. - **Kirilična forma:** `систем изводжења` - **Argumentacija / rationale:** The phrase transparently composes the standardized derivation noun izvodženje with the established system head and distinguishes the system from a proof, rule, or conclusion. - **Uvěrjenost / status:** 0.69 (medium); `provisional`; revision `OLISV-T0078-r0001`. - **Slovjanske sravnenja / comparanda:** ru: система вывода; uk: система виведення; pl: system wnioskowania; system dedukcyjny; cs: odvozovací systém; bcs: sistem izvođenja; bg: система за извод. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[5013-5015]; dictionary_id=17598,36763,36764); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** sistem vyvoda: A strong East-Slavic alternative, but vyvod can name the output while izvodženje directly names the derivation activity.; deduktivny sistem: This would narrow every derivation system to the deduction family. - **Neizvěstnost / uncertainty:** No frozen row directly attests the complete specialist compound.; The edition retains pravilo vyvoda for inference rule, so the lexical distinction must remain explicit. ## OLISV-T0080 · proof.derive - **English lemma / sense:** derive — To obtain a conclusion from premises by a derivation licensed by a specified formal proof system. - **Medžuslovjansky:** `izvoditi`; lemma `izvoditi`; transitive imperfective verb. - **Upotrěbljenje / inflection:** Use izvoditi imperfectively and izvesti perfectively; do not replace the formal relation with dokazati. - **Kirilična forma:** `изводити` - **Argumentacija / rationale:** The direct aspect pair izvoditi–izvesti has broad Slavic support and expresses derivation from premises without conflating it with semantic truth. - **Uvěrjenost / status:** 0.82 (high); `provisional`; revision `OLISV-T0080-r0001`. - **Slovjanske sravnenja / comparanda:** ru: выводить; uk: виводити; pl: wywodzić; dedukować; cs: vyvozovat; odvozovat; bcs: izvoditi; bg: извеждам. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[5014-5015]; dictionary_id=36763,36764); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** dokazati: Prove is broader than one derivation step or relation.; zaključiti: Infer or conclude foregrounds the result rather than the licensed derivation. - **Neizvěstnost / uncertainty:** The verbs also cover ordinary inference; proof-system context supplies the formal restriction. ## OLISV-T0145 · proof.induction-basis - **English lemma / sense:** induction basis — The base-constructor part of an induction proof, established before the preservation steps. - **Medžuslovjansky:** `baza indukcije`; lemma `baza indukcije`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive bazy indukcije; use for the base cases of the proof, not for a vector-space basis. - **Kirilična forma:** `база индукције` - **Argumentacija / rationale:** The international proof label is immediately recognizable and structurally converges across all six comparison traditions. - **Uvěrjenost / status:** 0.88 (high); `provisional`; revision `OLISV-T0145-r0001`. - **Slovjanske sravnenja / comparanda:** ru: база индукции; uk: база індукції; pl: baza indukcji; cs: báze indukce; bcs: baza indukcije; база индукције; bg: база на индукцията. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[1702]; dictionary_id=156); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** zaklad indukcije: The native head is transparent and retained as an alternative, but the international phrase is more uniform across the source-facing specialist traditions. - **Neizvěstnost / uncertainty:** The frozen dictionary row for baza records a military-base sense; the proof-theoretic specialization is supported by the source and comparanda rather than that row alone. ## OLISV-T0146 · proof.induction-hypothesis - **English lemma / sense:** induction hypothesis — The temporary assumption that the property holds for already constructed immediate components in an induction step. - **Medžuslovjansky:** `indukcijsko prědpoloženje`; lemma `indukcijsko prědpoloženje`; neuter noun phrase. - **Upotrěbljenje / inflection:** Genitive indukcijskogo prědpoloženja; instrumental indukcijskym prědpoloženjem; distinguish the proof assumption from an unproved research conjecture. - **Kirilična forma:** `индукцијско прєдположење` - **Argumentacija / rationale:** The supposition head directly bridges East, Czech, BCS, and Bulgarian terminology and makes the operational assumption sense explicit. - **Uvěrjenost / status:** 0.86 (high); `provisional`; revision `OLISV-T0146-r0001`. - **Slovjanske sravnenja / comparanda:** ru: индукционное предположение; uk: індукційне припущення; pl: założenie indukcyjne; cs: indukční předpoklad; bcs: indukcijska pretpostavka; индукцијска претпоставка; bg: индукционно предположение. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[16643]; dictionary_id=11247); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** indukcijska hipoteza: The international alternative is highly recognizable but can also denote a conjecture; it remains a documented searchable synonym. - **Neizvěstnost / uncertainty:** Polish and some textbooks prefer a hypothesis/assumption adjective phrase rather than a supposition noun. ## OLISV-T0170 · proof.inductive-step - **English lemma / sense:** inductive step — The part of an induction proof that derives the property for a constructed object from the induction hypotheses for its immediate components. - **Medžuslovjansky:** `indukcijski krok`; lemma `indukcijski krok`; masculine noun phrase. - **Upotrěbljenje / inflection:** Genitive indukcijskogo kroka and locative v indukcijskom kroku. The adjective follows canonical indukcijsko prědpoloženje (OLISV-T0146). - **Kirilična forma:** `индукцијски крок` - **Argumentacija / rationale:** Krok maximizes West/East lexical transparency while the already canonical induction adjective family keeps this obligation visibly paired with indukcijsko prědpoloženje; South-Slavic korak and Bulgarian stăpka remain documented divergences. - **Uvěrjenost / status:** 0.79 (medium); `provisional`; revision `OLISV-T0170-r0001`. - **Slovjanske sravnenja / comparanda:** ru: индукционный шаг; uk: індукційний крок; pl: krok indukcyjny; cs: indukční krok; bcs: indukcijski korak; индукцијски корак; bg: индукционна стъпка. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[16261]; dictionary_id=852; lemma=krok; gloss=step); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** indukcijny krok: The productive -ijny form is intelligible, but indukcijski preserves the adjective family already frozen in OLISV-T0146 and aligns directly with BCS technical morphology. - **Neizvěstnost / uncertainty:** East and South Slavic traditions do not share the selected krok head uniformly.; Both indukcijski and indukcijny are morphologically transparent; the choice is an edition consistency policy. ## OLISV-T0057 · proof.inference-rule - **English lemma / sense:** rule of inference — A licensed rule that extends a derivation or tableau from specified premises to specified conclusions. - **Medžuslovjansky:** `pravilo vyvoda`; lemma `pravilo vyvoda`; noun phrase. - **Upotrěbljenje / inflection:** Neuter head noun with genitive singular vyvoda; use pravila vyvoda in the plural. - **Kirilična forma:** `правило вывода` - **Argumentacija / rationale:** Pravilo vyvoda directly names a rule governing inferential output and is immediately recognizable in East Slavic, while remaining compositional for readers accustomed to West or South Slavic alternatives. - **Uvěrjenost / status:** 0.69 (medium); `provisional`; revision `OLISV-T0057-r0001`. - **Slovjanske sravnenja / comparanda:** ru: правило вывода; uk: правило виводу; pl: reguła wnioskowania; cs: odvozovací pravidlo; bcs: pravilo izvođenja; bg: правило за извод. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** pravilo zaključenja: Zaključenje can denote either the act or its conclusion and is less stable across proof systems than the established edition head vyvod. - **Neizvěstnost / uncertainty:** West and South Slavic traditions often lexicalize inference with wnioskowanie, odvození, or izvođenje rather than a vyvod cognate. ## OLISV-T0379 · proof.mathematical-induction - **English lemma / sense:** mathematical induction — The ordinary induction proof principle with a base case at zero and a successor step from the case n to n+1; it is distinct from complete or strong induction and from an induction axiom schema as a theory component. - **Medžuslovjansky:** `matematična indukcija`; lemma `matematična indukcija`; feminine adjective-noun phrase. - **Upotrěbljenje / inflection:** Feminine nominative matematična indukcija; instrumental matematičnoju indukcijeju. In concise proof prose, po indukciji is acceptable once the method is active. - **Kirilična forma:** `математична индукција` - **Argumentacija / rationale:** Matematična indukcija combines the official adjective with the international noun used consistently across the direct Ukrainian, Polish, and Croatian sources. The sense is deliberately limited to ordinary base-plus-successor induction; strong induction and an axiom schema remain separate canon concepts. - **Uvěrjenost / status:** 0.95 (high); `provisional`; revision `OLISV-T0379-r0001`. - **Slovjanske sravnenja / comparanda:** ru: математическая индукция; uk: математична індукція; pl: indukcja matematyczna; cs: matematická indukce; bcs: matematička indukcija; математичка индукција; bg: математическа индукция. - **Dokazy / evidence:** OL-MODEL-ARITHMETIC-STANDARD-MODELS (lines 132-150); ISV-DICT-LIVE-20260825 (wordList[10839]; dictionary_id=36602; lemma=matematičny; gloss=mathematical); RU-MI-RAS-PROVABILITY-ARITHMETIC-2020 (physical page 1 / extracted lines 22-24); UK-KNU-LOGIC-FOUNDATIONS-2020 (physical page 43 / extracted lines 1869-1880); PL-WROCLAW-THREE-INDUCTIONS-2012 (physical page 2 / extracted lines 68-96); HR-ZAGREB-SET-THEORY-INDUCTION (physical page 22 / extracted lines 822-843); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic, standard flavorization) - **Alternativy / alternatives:** polna indukcija: This names complete or strong induction in some Slavic traditions and would misclassify the ordinary proof in OLP-0193.; indukcijska metoda: A descriptive phrase is possible, but it obscures the standard specialist head directly shared across Ukrainian, Polish, and Croatian sources. - **Neizvěstnost / uncertainty:** The noun indukcija is a transparent cross-Slavic internationalism but is absent as a standalone head in the pinned Interslavic dictionary response.; This entry does not cover complete/strong induction or a theory's induction axiom schema. ## OLISV-T0014 · proof.proof - **English lemma / sense:** proof — A mathematical or formal argument establishing a conclusion from stated grounds. - **Medžuslovjansky:** `dokaz`; lemma `dokaz`; masculine noun. - **Upotrěbljenje / inflection:** Masculine noun; genitive singular dokaza, nominative plural dokazy. Use formalny dokaz when distinguishing a formal derivation from informal argument. - **Kirilična forma:** `доказ` - **Argumentacija / rationale:** Dokaz is directly dictionary-backed, maximally transparent across the comparison languages, and repeatedly inherited in formal mathematical prose. - **Uvěrjenost / status:** 0.99 (high); `seed_preferred`; revision `OLISV-T0014-r0001`. - **Slovjanske sravnenja / comparanda:** ru: доказательство; uk: доказ; pl: dowód; cs: důkaz; bcs: dokaz; bg: доказателство. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[12886]; dictionary_id=2041); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** dokazanje: The process noun can describe the act of proving, but Open Logic’s countable proof object is better served by the established head noun dokaz. - **Neizvěstnost / uncertainty:** No specific uncertainty beyond the provisional edition boundary. ## OLISV-T0245 · proof.recursion - **English lemma / sense:** recursion — The method defining a function successively from a base value and a successor clause. - **Medžuslovjansky:** `rekursija`; lemma `rekursija`; feminine noun. - **Upotrěbljenje / inflection:** Genitive rekursije; use obyčajna rekursija and rekursivno opreděliti where an adjective is needed. - **Kirilična forma:** `рекурсија` - **Argumentacija / rationale:** Rekursija is the broadly recognizable international mathematical noun and matches the source's base-and-successor construction. It is provisional because the bounded dictionary snapshot contains no direct recursion row. - **Uvěrjenost / status:** 0.74 (medium); `provisional`; revision `OLISV-T0245-r0002`. - **Slovjanske sravnenja / comparanda:** ru: рекурсия; uk: рекурсія; pl: rekurencja; cs: rekurze; bcs: rekurzija; рекурзија; bg: рекурсия. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (dictionary_id=17215; lemma=čislo; gloss=number); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** povtorno opreděljenje: An explanatory paraphrase, not the standard mathematical method name.; indukcija: Induction proves properties; it does not define the function in this passage. - **Neizvěstnost / uncertainty:** Polish and Czech prefer their own established cognates; the international form is chosen for cross-Slavic recognition.; The r0001 record remains preserved as adverse provenance for the target/source locator mismatch. ## OLISV-T0180 · proof.redundant-axiom - **English lemma / sense:** redundant axiom — An axiom that is already a semantic consequence of the other axioms in the system and can therefore be removed without changing semantic closure. - **Medžuslovjansky:** `izlišnja aksioma`; lemma `izlišnja aksioma`; feminine noun phrase. - **Upotrěbljenje / inflection:** The feminine adjective izlišnja agrees with aksioma; use genitive izlišnjoj aksiomy and plural izlišnje aksiomy. - **Kirilična forma:** `излишња аксиома` - **Argumentacija / rationale:** Izlišnja aksioma uses the frozen adjective that explicitly includes redundant in its gloss and is especially transparent to South Slavic and Bulgarian readers. Open Logic's formula supplies the formal meaning and prevents the ordinary adjective from remaining vague. - **Uvěrjenost / status:** 0.83 (high); `provisional`; revision `OLISV-T0180-r0001`. - **Slovjanske sravnenja / comparanda:** ru: избыточная аксиома; uk: зайва аксіома; pl: zbędny aksjomat; cs: nadbytečný axiom; bcs: suvišan aksiom; bg: излишна аксиома. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[16607]; dictionary_id=27228; lemma=izlišnji, izlišny; gloss=superfluous, redundant, excess); ISV-DICT-LIVE-20260825 (wordList[1498]; dictionary_id=24180; lemma=aksioma; gloss=axiom); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** izbytočna aksioma: The izbyt- family is strong in Russian and West Slavic, but the separately frozen izlišny row directly includes redundant, reaches South Slavic and Bulgarian more transparently, and is selected for the edition. - **Neizvěstnost / uncertainty:** National terminology divides between izbyt-/nadbyt- and izliš-/suviš- adjective families. ## OLISV-T0175 · proof.semantic-deduction-theorem - **English lemma / sense:** semantic deduction theorem — The semantic equivalence between entailment of B from Gamma together with A and entailment of the conditional A implies B from Gamma alone. - **Medžuslovjansky:** `semantična teorema dedukcije`; lemma `semantična teorema dedukcije`; feminine named-theorem noun phrase. - **Upotrěbljenje / inflection:** Genitive semantičnoj teoremy dedukcije. Keep semantična explicit: the result concerns semantic entailment, not a derivability rule inside a proof calculus. - **Kirilična forma:** `семантична теорема дедукције` - **Argumentacija / rationale:** Semantična teorema dedukcije transparently composes the already canonical semantic and deduction families and follows the edition's established feminine teorema naming policy. The explicit semantic modifier prevents confusion with the syntactic deduction theorem, while the dedicated canon ID pins the exact entailment biconditional. - **Uvěrjenost / status:** 0.92 (high); `provisional`; revision `OLISV-T0175-r0001`. - **Slovjanske sravnenja / comparanda:** ru: семантическая теорема о дедукции; uk: семантична теорема дедукції; pl: semantyczne twierdzenie o dedukcji; cs: sémantická věta o dedukci; bcs: semantički teorem dedukcije; семантичка теорема дедукције; bg: семантична теорема за дедукцията. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[15062]; dictionary_id=35935; lemma=semantika; gloss=semantics); ISV-DICT-LIVE-20260825 (wordList[4819]; dictionary_id=25162; lemma=dedukcija; gloss=deduction); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** semantičny teorem dedukcije: The masculine South-Slavic-facing variant is intelligible, but it conflicts with the edition's established feminine teorema construction for named mathematical results.; dedukcijska teorema: Without semantična this can denote a theorem internal to a deduction calculus and therefore erases the source's semantic/syntactic boundary.; teorema semantičnogo slědovanja: This describes the surrounding consequence relation but suppresses the recognized deduction-theorem identity and its bridge from an added premise to implication. - **Neizvěstnost / uncertainty:** No frozen Interslavic dictionary row directly attests the complete named theorem.; National traditions vary between theorem nouns and linking constructions; the selected phrase follows the edition's established naming policy. ## OLISV-T0058 · proof.soundness - **English lemma / sense:** soundness — The property that a proof system derives only semantically valid consequences. - **Medžuslovjansky:** `korektnost`; lemma `korektnost`; noun. - **Upotrěbljenje / inflection:** Feminine abstract noun; use korektny for the corresponding adjective and teorema korektnosti for the theorem. - **Kirilična forma:** `коректност` - **Argumentacija / rationale:** Korektnost matches the established mathematical sense in several Slavic traditions and avoids the misleading literal calque of English soundness as an acoustic or physical property. - **Uvěrjenost / status:** 0.81 (high); `provisional`; revision `OLISV-T0058-r0001`. - **Slovjanske sravnenja / comparanda:** ru: корректность; uk: коректність; pl: poprawność; cs: korektnost; bcs: korektnost; bg: коректност. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** zdravost: A literal calque of English soundness suggests health or physical integrity and obscures the semantic-preservation theorem. - **Neizvěstnost / uncertainty:** Polish specialist usage prefers poprawność, so the selected international form is not equally native-looking across all Slavic readerships. ## OLISV-T0152 · proof.strong-induction - **English lemma / sense:** strong induction — Induction on a natural-number index whose step may use the claim for every strictly smaller index. - **Medžuslovjansky:** `silna indukcija`; lemma `silna indukcija`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive silnoj indukcije; in this unit the induction parameter is the final index of a formation sequence, not its ordinary length. - **Kirilična forma:** `силна индукција` - **Argumentacija / rationale:** Silna indukcija directly mirrors the source label and converges across the East-Slavic and Bulgarian comparanda while remaining transparent elsewhere. It also prevents confusion with strukturna indukcija, which the preceding proof applies to formula construction rather than to a numerical index. - **Uvěrjenost / status:** 0.84 (medium); `provisional`; revision `OLISV-T0152-r0001`. - **Slovjanske sravnenja / comparanda:** ru: сильная индукция; uk: сильна індукція; pl: silna indukcja; cs: silná indukce; bcs: jaka indukcija; јака индукција; bg: силна индукция. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-DICT-LIVE-20260825 (wordList[16423]; dictionary_id=1310); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** polna indukcija: This West-Slavic synonym family is recognizable, but it obscures the source's explicit strong label and risks collision with the canon's separate polnota terminology.; strukturna indukcija: That canonical term applies to induction over generated syntax; the present proof is numerical induction on the final sequence index. - **Neizvěstnost / uncertainty:** West-Slavic textbooks may prefer complete-induction terminology, while South-Slavic sources may use jaka rather than silna.; The source proof confuses final index and sequence length; the translation states the valid final-index induction explicitly.; No official or native certification is claimed for the complete specialist compound. ## OLISV-T0138 · proof.structural-induction - **English lemma / sense:** structural induction — An induction principle proving a property for every inductively generated expression by covering the base constructors and preserving constructors. - **Medžuslovjansky:** `strukturna indukcija`; lemma `strukturna indukcija`; feminine noun phrase. - **Upotrěbljenje / inflection:** Genitive strukturnoj indukcije; the source instantiates it separately for terms and formulas. - **Kirilična forma:** `структурна индукција` - **Argumentacija / rationale:** The international compound is identical or trivially adapted throughout the six specialist traditions and already occurs pedagogically in the accepted edition. - **Uvěrjenost / status:** 0.94 (high); `provisional`; revision `OLISV-T0138-r0001`. - **Slovjanske sravnenja / comparanda:** ru: структурная индукция; uk: структурна індукція; pl: indukcja strukturalna; cs: strukturální indukce; bcs: strukturna indukcija; структурна индукција; bg: структурна индукция. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[16425]; dictionary_id=36307); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** občna indukcija: The generic label loses the essential induction-on-construction-structure restriction. - **Neizvěstnost / uncertainty:** The frozen dictionary attests only the adjective, not the complete proof-theoretic compound. ## OLISV-T0055 · proof.tableau - **English lemma / sense:** tableau proof — A tree of signed formulas generated by inference rules and used to test whether every branch closes. - **Medžuslovjansky:** `tabelarny dokaz`; lemma `tabelarny dokaz`; noun phrase. - **Upotrěbljenje / inflection:** Masculine noun phrase; tabelarny agrees with dokaz. The source macro tableau remains unchanged where the build system requires it. - **Kirilična forma:** `табеларны доказ` - **Argumentacija / rationale:** Tabelarny transparently connects the method to a table-like branching display, while dokaz keeps the practical proof function explicit for Slavic readers who may not know the borrowed French-English label tableau. - **Uvěrjenost / status:** 0.64 (medium); `provisional`; revision `OLISV-T0055-r0001`. - **Slovjanske sravnenja / comparanda:** ru: табличное доказательство; uk: табличний доказ; pl: dowód tablicowy; cs: tabulkový důkaz; bcs: tablični dokaz; bg: таблично доказателство. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** tableau: The unadapted loan is opaque to many Slavic readers and is retained only as a protected source macro where technically required. - **Neizvěstnost / uncertainty:** The national traditions distribute this concept across table, tableau, and semantic-tree terminology; the edition compound prioritizes transparent function over one national convention. ## OLISV-T0029 · relation.antisymmetric - **English lemma / sense:** antisymmetric relation — A relation R for which Rxy and Ryx together imply x equals y. - **Medžuslovjansky:** `antisimetrično odnošenje`; lemma `antisimetrično odnošenje`; noun phrase. - **Upotrěbljenje / inflection:** Neuter adjective agrees with odnošenje; write anti- as a bound international prefix in antisimetrično. - **Kirilična forma:** `антисиметрично одношење` - **Argumentacija / rationale:** Direct relation component, productive international prefixation, regular agreement, and cross-Slavic convergence. The English definition at OL-REL-PROPERTIES lines 38-42 fixes the intended sense; this revision selects an edition term without asserting official or native certification. - **Uvěrjenost / status:** 0.7 (medium); `provisional`; revision `OLISV-T0029-r0001`. - **Slovjanske sravnenja / comparanda:** ru: антисимметричное отношение; uk: антисиметричне відношення; pl: relacja antysymetryczna; cs: antisymetrická relace; bcs: antisimetrična relacija; bg: антисиметрично отношение. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[14174]; dictionary_id=1992); ISV-GRAMMAR-ADJ (lines 14-18); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** protivosimetrično odnošenje: The hybrid calque is less recognizable than the international anti- formation shared by the comparison languages. - **Neizvěstnost / uncertainty:** The complete prefixed specialist compound is editorial and absent from the bounded official dictionary evidence.; Cross-Slavic specialist surfaces are editorial comparanda from the bounded evidence review and are not represented as official or native-certified forms. ## OLISV-T0032 · relation.asymmetric - **English lemma / sense:** asymmetric relation — A relation R for which no pair x and y satisfies both Rxy and Ryx. - **Medžuslovjansky:** `asimetrično odnošenje`; lemma `asimetrično odnošenje`; noun phrase. - **Upotrěbljenje / inflection:** Neuter adjective agrees with odnošenje; distinguish asimetrično from antisimetrično. - **Kirilična forma:** `асиметрично одношење` - **Argumentacija / rationale:** Direct relation component, regular international adjective, and a stable logical contrast across comparanda. The English definition at OL-REL-PROPERTIES lines 74-77 fixes the intended sense; this revision selects an edition term without asserting official or native certification. - **Uvěrjenost / status:** 0.7 (medium); `provisional`; revision `OLISV-T0032-r0001`. - **Slovjanske sravnenja / comparanda:** ru: асимметричное отношение; uk: асиметричне відношення; pl: relacja asymetryczna; cs: asymetrická relace; bcs: asimetrična relacija; bg: асиметрично отношение. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[14174]; dictionary_id=1992); ISV-GRAMMAR-ADJ (lines 14-18); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** nesimetrično odnošenje: Nesimetrično says only that symmetry fails and does not express the stronger asymmetric condition. - **Neizvěstnost / uncertainty:** No bounded official dictionary row directly attests the complete specialist compound.; Cross-Slavic specialist surfaces are editorial comparanda from the bounded evidence review and are not represented as official or native-certified forms. ## OLISV-T0042 · relation.branch - **English lemma / sense:** branch of a tree — A maximal chain in a tree. - **Medžuslovjansky:** `větva`; lemma `větva`; noun. - **Upotrěbljenje / inflection:** Feminine noun; genitive singular větvy and nominative plural větvy. Use with a genitive tree phrase when needed. - **Kirilična forma:** `вєтва` - **Argumentacija / rationale:** Transparent East/West Slavic cognacy but substantial lexical divergence in Ukrainian, Polish, BCS, and Bulgarian. The English definition at OL-REL-TREES lines 90-98 fixes the intended sense; this revision selects an edition term without asserting official or native certification. - **Uvěrjenost / status:** 0.61 (medium); `provisional`; revision `OLISV-T0042-r0001`. - **Slovjanske sravnenja / comparanda:** ru: ветвь; uk: гілка; pl: gałąź; cs: větev; bcs: grana; bg: клон. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** grana: Grana is natural in BCS but větva provides stronger Russian and Czech cognacy and matches the edition's tree terminology. - **Neizvěstnost / uncertainty:** No bounded official dictionary row attests větva in the order-theoretic tree sense.; Cross-Slavic specialist surfaces are editorial comparanda from the bounded evidence review and are not represented as official or native-certified forms. ## OLISV-T0030 · relation.connected - **English lemma / sense:** connected relation — A relation R on A such that distinct x and y are related in at least one direction. - **Medžuslovjansky:** `povezano odnošenje`; lemma `povezano odnošenje`; noun phrase. - **Upotrěbljenje / inflection:** Neuter adjective agrees with odnošenje; this connectedness sense is local to order relations and should not replace graph connectivity terminology automatically. - **Kirilična forma:** `повезано одношење` - **Argumentacija / rationale:** Direct relation component and transparent native derivation, but comparison languages divide between connection stems. The English definition at OL-REL-PROPERTIES lines 57-60 fixes the intended sense; this revision selects an edition term without asserting official or native certification. - **Uvěrjenost / status:** 0.6 (medium); `provisional`; revision `OLISV-T0030-r0001`. - **Slovjanske sravnenja / comparanda:** ru: связное отношение; uk: зв'язне відношення; pl: relacja spójna; cs: souvislá relace; bcs: povezana relacija; bg: свързано отношение. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[14174]; dictionary_id=1992); ISV-GRAMMAR-ADJ (lines 14-18); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** spojeno odnošenje: Spojeno risks a physical-joining reading; povezano follows the edition's relational formulation more transparently. - **Neizvěstnost / uncertainty:** The specialist sense of povezano is an editorial normalization with material cross-Slavic lexical divergence.; Cross-Slavic specialist surfaces are editorial comparanda from the bounded evidence review and are not represented as official or native-certified forms. ## OLISV-T0360 · relation.dense-order - **English lemma / sense:** dense order — An order in which, whenever x is strictly below y, some z lies strictly between x and y. - **Medžuslovjansky:** `gųsty poredok`; lemma `gųsty poredok`; masculine adjective-noun phrase. - **Upotrěbljenje / inflection:** Masculine adjective agrees with poredok; plural gųste poredky, genitive plural gųstyh poredkov. Use gųstosť poredka for the abstract property. - **Kirilična forma:** `густы поредок` - **Argumentacija / rationale:** The official dictionary head gųsty converges with Polish gęsty and Croatian gust while remaining recognizable beside Russian плотный. The exact Open Logic axiom and three independently preserved academic witnesses prevent the everyday thick/dense meaning from replacing the order-theoretic one. Existing OLISV-T0038 supplies linearny poredok where the fuller subtype is needed. - **Uvěrjenost / status:** 0.92 (high); `provisional`; revision `OLISV-T0360-r0001`. - **Slovjanske sravnenja / comparanda:** ru: плотный линейный порядок; uk: щільний лінійний порядок; pl: porządek gęsty; cs: husté uspořádání; bcs: gust linearno uređen skup; bg: гъста линейна наредба. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (dictionary_id=5308, gųsty, gloss dense/thick, with all major Slavic comparison columns); OL-MODEL-DENSE-LINEAR-ORDER (lines 10-26, axiom 6); RU-MI-RAS-DENSE-LINEAR-ORDER-2015 (physical PDF page 12, problem 10); PL-PW-DENSE-LINEAR-ORDER-2022 (physical/printed PDF page 23, Zadanie 181); HR-ZAGREB-DENSE-LINEAR-ORDER-2015 (physical PDF page 50, printed page 46, Definition 1.75); ISV-TRANSLIT-3.4.4 (package/dist/index.browser.min.js; isv-Cyrl) - **Alternativy / alternatives:** plotny poredok: Plotny closely follows Russian but loses the direct West- and South-Slavic convergence and the official Interslavic dictionary head.; gųstotny poredok: An abstract-noun derivative is unnecessary and less directly recognizable than the official adjective gųsty. - **Neizvěstnost / uncertainty:** The official dictionary supports the general adjective rather than independently standardizing its order-theoretic sense.; Ukrainian, Czech, and Bulgarian full phrases are transparent editorial comparanda, not direct attestations. ## OLISV-T0040 · relation.directed-graph - **English lemma / sense:** directed graph — A pair consisting of a vertex set V and an edge relation E contained in V squared. - **Medžuslovjansky:** `orientovany graf`; lemma `orientovany graf`; noun phrase. - **Upotrěbljenje / inflection:** Masculine adjective agrees with graf; genitive singular orientovanogo grafa and nominative plural orientovane grafy. - **Kirilična forma:** `ориентованы граф` - **Argumentacija / rationale:** International graph stem and broad comparison-language recognition, with transparent regular adjective agreement. The English definition at OL-REL-GRAPHS lines 24-27 fixes the intended sense; this revision selects an edition term without asserting official or native certification. - **Uvěrjenost / status:** 0.68 (medium); `provisional`; revision `OLISV-T0040-r0001`. - **Slovjanske sravnenja / comparanda:** ru: ориентированный граф; uk: орієнтований граф; pl: graf skierowany; cs: orientovaný graf; bcs: usmjereni graf; bg: ориентиран граф. - **Dokazy / evidence:** ISV-GRAMMAR-ADJ (lines 14-18); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** usměrjeny graf: The native direction calque is strong in Polish and BCS, but orientovany maximizes direct recognition in East Slavic, Czech, and Bulgarian. - **Neizvěstnost / uncertainty:** No bounded official dictionary row directly attests orientovany graf.; Cross-Slavic specialist surfaces are editorial comparanda from the bounded evidence review and are not represented as official or native-certified forms. ## OLISV-T0033 · relation.equivalence - **English lemma / sense:** equivalence relation — A relation that is reflexive, symmetric, and transitive. - **Medžuslovjansky:** `odnošenje ekvivalentnosti`; lemma `odnošenje ekvivalentnosti`; noun phrase. - **Upotrěbljenje / inflection:** Use ekvivalentnost in the genitive singular after odnošenje; decline odnošenje as the head noun. - **Kirilična forma:** `одношење еквивалентности` - **Argumentacija / rationale:** Direct relation lemma plus inherited mathematical ekvivalentnost and klasa usage in an adjacent classification context. The English definition at OL-REL-EQUIVALENCE lines 17-21 fixes the intended sense; this revision selects an edition term without asserting official or native certification. - **Uvěrjenost / status:** 0.8 (high); `provisional`; revision `OLISV-T0033-r0001`. - **Slovjanske sravnenja / comparanda:** ru: отношение эквивалентности; uk: відношення еквівалентності; pl: relacja równoważności; cs: relace ekvivalence; bcs: relacija ekvivalencije; bg: отношение на еквивалентност. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[14174]; dictionary_id=1992); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** ekvivalentno odnošenje: The genitive construction more clearly names the relation type and matches the edition's selected heading. - **Neizvěstnost / uncertainty:** No bounded official dictionary row attests the full relation-theoretic compound.; Cross-Slavic specialist surfaces are editorial comparanda from the bounded evidence review and are not represented as official or native-certified forms. ## OLISV-T0034 · relation.equivalence-class - **English lemma / sense:** equivalence class — For x under an equivalence relation R, the set of all y such that Rxy. - **Medžuslovjansky:** `klasa ekvivalentnosti`; lemma `klasa ekvivalentnosti`; noun phrase. - **Upotrěbljenje / inflection:** Use ekvivalentnost in the genitive singular after klasa; plural is klasy ekvivalentnosti. - **Kirilična forma:** `класа еквивалентности` - **Argumentacija / rationale:** Inherited mathematical use combines klasa with ekvivalentny, while the Open Logic definition fixes the set-theoretic sense. The English definition at OL-REL-EQUIVALENCE lines 31-36 fixes the intended sense; this revision selects an edition term without asserting official or native certification. - **Uvěrjenost / status:** 0.78 (high); `provisional`; revision `OLISV-T0034-r0001`. - **Slovjanske sravnenja / comparanda:** ru: класс эквивалентности; uk: клас еквівалентності; pl: klasa abstrakcji; cs: třída ekvivalence; bcs: klasa ekvivalencije; bg: клас на еквивалентност. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[14174]; dictionary_id=1992); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** razred ekvivalentnosti: Razred is viable in part of South Slavic, but klasa has stronger inherited mathematical continuity in the selected corpus. - **Neizvěstnost / uncertainty:** The exact compound klasa ekvivalentnosti is not directly attested in the bounded official dictionary source.; Cross-Slavic specialist surfaces are editorial comparanda from the bounded evidence review and are not represented as official or native-certified forms. ## OLISV-T0216 · relation.functional - **English lemma / sense:** functional relation — A right-unique relation: for each first coordinate, any two related second coordinates are equal. - **Medžuslovjansky:** `funkcionalno odnošenje`; lemma `funkcionalno odnošenje`; neuter adjective-noun phrase. - **Upotrěbljenje / inflection:** Neuter adjective-noun agreement; genitive funkcionalnogo odnošenja and plural funkcionalna odnošenja. - **Kirilična forma:** `функционално одношење` - **Argumentacija / rationale:** The phrase is morphologically regular, strongly convergent across the comparison languages, and already anchored by an accepted graph-of-function explanation. - **Uvěrjenost / status:** 0.91 (high); `provisional`; revision `OLISV-T0216-r0001`. - **Slovjanske sravnenja / comparanda:** ru: функциональное отношение; uk: функціональне відношення; pl: relacja funkcyjna; cs: funkční relace; bcs: funkcionalna relacija; bg: функционално отношение. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[7435]; dictionary_id=35303; lemma=funkcionaľny; gloss=functional); ISV-DICT-LIVE-20260825 (wordList[14174]; dictionary_id=1992; lemma=odnošeńje; gloss=relation); OL-FUN-RELATIONS-ISV (lines 14-51); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** funkcijno odnošenje: Funkcijno can be understood compositionally, but it is less standard for the technical right-unique property and conflicts with the accepted funkcionalno precedent. - **Neizvěstnost / uncertainty:** This property is right-uniqueness only; totality is a separate canon entry and must not be inferred from functional alone. ## OLISV-T0043 · relation.inverse - **English lemma / sense:** inverse relation — The relation obtained by reversing every ordered pair in a relation. - **Medžuslovjansky:** `obratno odnošenje`; lemma `obratno odnošenje`; noun phrase. - **Upotrěbljenje / inflection:** Neuter adjective agrees with odnošenje; the relational context distinguishes it from obratna funkcija. - **Kirilična forma:** `обратно одношење` - **Argumentacija / rationale:** Direct official relation component and broad cross-Slavic support for either the selected native stem or a close inverse synonym. The English definition at OL-REL-OPERATIONS lines 19-24 fixes the intended sense; this revision selects an edition term without asserting official or native certification. - **Uvěrjenost / status:** 0.72 (medium); `provisional`; revision `OLISV-T0043-r0001`. - **Slovjanske sravnenja / comparanda:** ru: обратное отношение; uk: обернене відношення; pl: relacja odwrotna; cs: inverzní relace; bcs: inverzna relacija; bg: обратно отношение. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[14174]; dictionary_id=1992); ISV-GRAMMAR-ADJ (lines 14-18); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** inverzno odnošenje: The international alternative is strong in Czech and BCS, but obratno is immediately transparent in East Slavic and Bulgarian and aligns with inverse function. - **Neizvěstnost / uncertainty:** No bounded official row attests the complete inverse-relation phrase.; Cross-Slavic specialist surfaces are editorial comparanda from the bounded evidence review and are not represented as official or native-certified forms. ## OLISV-T0031 · relation.irreflexive - **English lemma / sense:** irreflexive relation — A relation R on A for which Rxx fails for every x in A. - **Medžuslovjansky:** `irefleksivno odnošenje`; lemma `irefleksivno odnošenje`; noun phrase. - **Upotrěbljenje / inflection:** Neuter adjective agrees with odnošenje; i- is retained as the conventional international negative prefix in this term. - **Kirilična forma:** `ирефлексивно одношење` - **Argumentacija / rationale:** Direct relation component and a semantically necessary international contrast with mere non-reflexivity. The English definition at OL-REL-PROPERTIES lines 69-72 fixes the intended sense; this revision selects an edition term without asserting official or native certification. - **Uvěrjenost / status:** 0.68 (medium); `provisional`; revision `OLISV-T0031-r0001`. - **Slovjanske sravnenja / comparanda:** ru: иррефлексивное отношение; uk: іррефлексивне відношення; pl: relacja przeciwzwrotna; cs: ireflexivní relace; bcs: irefleksivna relacija; bg: ирефлексивно отношение. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[14174]; dictionary_id=1992); ISV-GRAMMAR-ADJ (lines 14-18); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** nerefleksivno odnošenje: Nerefleksivno can mean merely not reflexive, whereas irreflexive requires failure at every diagonal pair. - **Neizvěstnost / uncertainty:** The bounded official sources do not directly attest the irefleksivno specialist adjective.; Cross-Slavic specialist surfaces are editorial comparanda from the bounded evidence review and are not represented as official or native-certified forms. ## OLISV-T0249 · relation.least-element - **English lemma / sense:** least element — The minimum member of a non-empty subset under the relevant ordering. - **Medžuslovjansky:** `najmenši element`; lemma `najmenši element`; masculine adjective-noun phrase. - **Upotrěbljenje / inflection:** Genitive najmenšego elementa; use najmenši element množstva for a scoped set. - **Kirilična forma:** `најменши елемент` - **Argumentacija / rationale:** Both components have direct dictionary support, and the source formula explicitly quantifies the least member. The head is retained as a phrase so agreement remains visible in prose. - **Uvěrjenost / status:** 0.94 (high); `provisional`; revision `OLISV-T0249-r0002`. - **Slovjanske sravnenja / comparanda:** ru: наименьший элемент; uk: найменший елемент; pl: najmniejszy element; cs: nejmenší prvek; bcs: najmanji element; најмањи елемент; bg: най-малък елемент. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (dictionary_id=9381; lemma=najmėnši; gloss=smallest); ISV-DICT-LIVE-20260825 (dictionary_id=17372; lemma=element; gloss=element); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** minimalny element: Minimalny is used for proof systems and does not necessarily mean least under an order.; najmėnje element: The adverb cannot modify a noun in this construction. - **Neizvěstnost / uncertainty:** Czech and some South-Slavic traditions use a root equivalent to first/minimum; the selected phrase remains broadly legible.; The r0001 record remains preserved as adverse provenance for the target/source locator mismatch. ## OLISV-T0038 · relation.linear-order - **English lemma / sense:** linear order — A connected partial order, also called a total order. - **Medžuslovjansky:** `linearny poredok`; lemma `linearny poredok`; noun phrase. - **Upotrěbljenje / inflection:** Masculine adjective agrees with poredok; polny poredok may be mentioned as a synonym, but linearny poredok is preferred. - **Kirilična forma:** `линеарны поредок` - **Argumentacija / rationale:** Inherited poredok component and near-universal comparison-language support for the linear adjective. The English definition at OL-REL-ORDERS lines 32-35 fixes the intended sense; this revision selects an edition term without asserting official or native certification. - **Uvěrjenost / status:** 0.7 (medium); `provisional`; revision `OLISV-T0038-r0001`. - **Slovjanske sravnenja / comparanda:** ru: линейный порядок; uk: лінійний порядок; pl: porządek liniowy; cs: lineární uspořádání; bcs: linearno uređenje; bg: линейна наредба. - **Dokazy / evidence:** ISV-GRAMMAR-ADJ (lines 14-18); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** polny poredok: The source gives total and linear order; linearny has the strongest six-language international convergence and avoids overloading polny. - **Neizvěstnost / uncertainty:** The complete phrase is not directly attested in the bounded official Interslavic dictionary evidence.; Cross-Slavic specialist surfaces are editorial comparanda from the bounded evidence review and are not represented as official or native-certified forms. ## OLISV-T0006 · relation.mathematical - **English lemma / sense:** relation — A set of ordered tuples, especially a binary relation represented as a subset of a Cartesian square. - **Medžuslovjansky:** `odnošenje`; lemma `odnošenje`; neuter noun. - **Upotrěbljenje / inflection:** The dictionary source form odnošeńje is normalized to standard/basic odnošenje. Use binarno odnošenje na množstvu A; genitive singular odnošenja. - **Kirilična forma:** `одношење` - **Argumentacija / rationale:** Odnošenje has direct dictionary support and inherited mathematical use, while preserving a transparent Slavic root. Context or the modifier binarno resolves its broader everyday senses. - **Uvěrjenost / status:** 0.86 (high); `seed_preferred`; revision `OLISV-T0006-r0001`. - **Slovjanske sravnenja / comparanda:** ru: отношение; uk: відношення; pl: relacja; cs: vztah; bcs: odnos, relacija; bg: отношение. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[14174]; dictionary_id=1992); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** relacija: Relacija is well established in the inherited mathematics and in West/South comparanda, but it has no direct lemma row in the bounded dictionary data; retain it as a searchable alternative. - **Neizvěstnost / uncertainty:** Specialist usage may favor relacija in some contexts; this seed chooses the directly dictionary-backed Slavic-rooted lemma. ## OLISV-T0362 · relation.order-endpoint - **English lemma / sense:** endpoint of a linear order — A least or greatest element of a linear order; not an arbitrary minimal or maximal element of a non-linear order. - **Medžuslovjansky:** `krajny element poredka`; lemma `krajny element poredka`; masculine adjective-noun phrase. - **Upotrěbljenje / inflection:** Genitive plural krajnyh elementov poredka. In definitions, identify the pair as najmenši i največši element to prevent confusion with non-linear minimal/maximal elements. - **Kirilična forma:** `крајны елемент поредка` - **Argumentacija / rationale:** Krajny is an official Interslavic dictionary lemma meaning extreme or utmost and yields the concise recurring phrase bez krajnyh elementov. Because national mathematical sources often prefer an explicit least/greatest formulation, the house usage always binds the term to najmenši i največši element at first definition. The definition is restricted to linear orders, where least/minimal and greatest/maximal coincide. - **Uvěrjenost / status:** 0.79 (medium); `provisional`; revision `OLISV-T0362-r0001`. - **Slovjanske sravnenja / comparanda:** ru: концевая точка линейного порядка; uk: найменший або найбільший елемент порядку; pl: element najmniejszy lub największy; cs: nejmenší nebo největší prvek uspořádání; bcs: najmanji ili najveći element; bg: най-малък или най-голям елемент на наредбата. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (dictionary_id=757, krajny, gloss extreme/utmost; inflection row krajnyh); OL-MODEL-DENSE-LINEAR-ORDER (lines 19-22); RU-KFU-DENSE-LINEAR-ORDER-2013 (physical PDF page 63, printed page 62); PL-PW-DENSE-LINEAR-ORDER-2022 (physical/printed PDF page 23); HR-ZAGREB-DENSE-LINEAR-ORDER-2015 (physical PDF page 52, printed page 48); ISV-TRANSLIT-3.4.4 (package/dist/index.browser.min.js; isv-Cyrl) - **Alternativy / alternatives:** konec poredka: Konec can suggest temporal termination or a physical end and does not transparently denote an element of the ordered domain.; graničny element: Boundary terminology risks a metric or topological reading and lacks the direct dictionary-plus-definition support of krajny element. - **Neizvěstnost / uncertainty:** The complete specialist phrase is synthesized rather than directly certified by an official Interslavic mathematical dictionary.; The concise head is safe only with the recorded linear-order sense and first-use least/greatest gloss. ## OLISV-T0037 · relation.partial-order - **English lemma / sense:** partial order — An antisymmetric preorder. - **Medžuslovjansky:** `čestičny poredok`; lemma `čestičny poredok`; noun phrase. - **Upotrěbljenje / inflection:** Masculine adjective agrees with poredok; decline the phrase regularly as masculine inanimate. - **Kirilična forma:** `честичны поредок` - **Argumentacija / rationale:** Inherited poredok component and strong East/West Slavic support for a part-based adjective, despite South Slavic variation. The English definition at OL-REL-ORDERS lines 27-30 fixes the intended sense; this revision selects an edition term without asserting official or native certification. - **Uvěrjenost / status:** 0.66 (medium); `provisional`; revision `OLISV-T0037-r0001`. - **Slovjanske sravnenja / comparanda:** ru: частичный порядок; uk: частковий порядок; pl: porządek częściowy; cs: částečné uspořádání; bcs: parcijalno uređenje; bg: частична наредба. - **Dokazy / evidence:** ISV-GRAMMAR-ADJ (lines 14-18); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** parcialny poredok: The international adjective is transparent in BCS, but čestičny offers broader East/West Slavic recognizability in this edition. - **Neizvěstnost / uncertainty:** No bounded official source attests čestičny poredok in the order-theoretic sense.; Cross-Slavic specialist surfaces are editorial comparanda from the bounded evidence review and are not represented as official or native-certified forms. ## OLISV-T0204 · relation.predecessor - **English lemma / sense:** predecessor relation — The binary arithmetic relation inverse to the successor relation, here expressed by equality to the successor of the second argument. - **Medžuslovjansky:** `odnošenje prědhodnika`; lemma `odnošenje prědhodnika`; neuter noun phrase with genitive singular. - **Upotrěbljenje / inflection:** Neuter head with genitive prědhodnika; the argument order is fixed by the displayed formula. - **Kirilična forma:** `одношење прєдходника` - **Argumentacija / rationale:** Both components are directly registered, and the complete term already occurs in an accepted mathematical unit. It also pairs transparently with odnošenje naslědnika. - **Uvěrjenost / status:** 0.89 (high); `provisional`; revision `OLISV-T0204-r0001`. - **Slovjanske sravnenja / comparanda:** ru: отношение предшественника; uk: відношення попередника; pl: relacja poprzednika; cs: relace předchůdce; bcs: relacija prethodnika; релација претходника; bg: отношение на предшественика. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[13288]; dictionary_id=35639; lemma=prědhodnik; gloss=predecessor); ISV-DICT-LIVE-20260825 (wordList[14174]; dictionary_id=1992; lemma=odnošeńje; gloss=relation); OL-REL-OPERATIONS-ISV (lines 40-43); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** odnošenje prědšestvennika: The East-Slavic-heavy alternative is less uniform and weaker than the direct frozen prědhodnik lemma and the established accepted-unit precedent. - **Neizvěstnost / uncertainty:** National traditions vary between predecessor-as-person and predecessor-as-number morphology, but the formal context removes referential ambiguity. ## OLISV-T0036 · relation.preorder - **English lemma / sense:** preorder — A relation that is reflexive and transitive. - **Medžuslovjansky:** `prědporedok`; lemma `prědporedok`; noun. - **Upotrěbljenje / inflection:** Masculine inanimate noun; genitive singular prědporedka and nominative plural prědporedky. - **Kirilična forma:** `прєдпоредок` - **Argumentacija / rationale:** Transparent derivation from inherited poredok and East Slavic convergence, with notable West and South Slavic variation. The English definition at OL-REL-ORDERS lines 22-25 fixes the intended sense; this revision selects an edition term without asserting official or native certification. - **Uvěrjenost / status:** 0.58 (medium); `provisional`; revision `OLISV-T0036-r0001`. - **Slovjanske sravnenja / comparanda:** ru: предпорядок; uk: передпорядок; pl: praporządek; cs: kvaziuspořádání; bcs: preduređenje; bg: предпорядък. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** kvaziporedok: Kvazi- is recognizable in Czech usage, but prěd- preserves the direct structural relation to poredok across East Slavic comparanda. - **Neizvěstnost / uncertainty:** No bounded official source directly attests prědporedok; comparison languages do not converge on one stem.; Cross-Slavic specialist surfaces are editorial comparanda from the bounded evidence review and are not represented as official or native-certified forms. ## OLISV-T0035 · relation.quotient-set - **English lemma / sense:** quotient set — The set of all equivalence classes of a set under an equivalence relation. - **Medžuslovjansky:** `kvocient množstva po odnošenju`; lemma `kvocient množstva po odnošenju`; noun phrase. - **Upotrěbljenje / inflection:** When the base set and relation are explicit, the short form kvocient is permitted; otherwise retain the full genitive phrase. - **Kirilična forma:** `квоциент множства по одношењу` - **Argumentacija / rationale:** Direct inherited mathematical use of kvocient plus a definition-bound compound that disambiguates the set-theoretic sense. The English definition at OL-REL-EQUIVALENCE lines 31-36 fixes the intended sense; this revision selects an edition term without asserting official or native certification. - **Uvěrjenost / status:** 0.72 (medium); `provisional`; revision `OLISV-T0035-r0001`. - **Slovjanske sravnenja / comparanda:** ru: фактор-множество; uk: фактор-множина; pl: zbiór ilorazowy; cs: faktorová množina; bcs: kvocijentni skup; bg: фактор-множество. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[14174]; dictionary_id=1992); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** faktorno množstvo: The factor-set calque is widespread but collides with factor terminology; kvocient has direct inherited mathematical support. - **Neizvěstnost / uncertainty:** Inherited kvocient examples are algebraic quotients, not this exact quotient-set construction.; Cross-Slavic specialist surfaces are editorial comparanda from the bounded evidence review and are not represented as official or native-certified forms. ## OLISV-T0026 · relation.reflexive - **English lemma / sense:** reflexive relation — A binary relation R on A for which Rxx holds for every x in A. - **Medžuslovjansky:** `refleksivno odnošenje`; lemma `refleksivno odnošenje`; noun phrase. - **Upotrěbljenje / inflection:** Neuter adjective agrees with odnošenje; use refleksivno odnošenje in the nominative and decline odnošenje regularly. - **Kirilična forma:** `рефлексивно одношење` - **Argumentacija / rationale:** Direct official support for odnošenje plus transparent specialist adjective and broad cross-Slavic convergence. The English definition at OL-REL-PROPERTIES lines 23-26 fixes the intended sense; this revision selects an edition term without asserting official or native certification. - **Uvěrjenost / status:** 0.72 (medium); `provisional`; revision `OLISV-T0026-r0001`. - **Slovjanske sravnenja / comparanda:** ru: рефлексивное отношение; uk: рефлексивне відношення; pl: relacja zwrotna; cs: reflexivní relace; bcs: refleksivna relacija; bg: рефлексивно отношение. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[14174]; dictionary_id=1992); ISV-GRAMMAR-ADJ (lines 14-18); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** samoodnosno odnošenje: A descriptive calque is less transparent across Slavic mathematical traditions than the international reflexive stem. - **Neizvěstnost / uncertainty:** No bounded official dictionary row attests the complete specialist compound.; Cross-Slavic specialist surfaces are editorial comparanda from the bounded evidence review and are not represented as official or native-certified forms. ## OLISV-T0044 · relation.relative-product - **English lemma / sense:** relative product of relations — For R and S, the relation containing x,z when some y satisfies Rxy and Syz. - **Medžuslovjansky:** `relativny produkt odnošenij`; lemma `relativny produkt odnošenij`; noun phrase. - **Upotrěbljenje / inflection:** Use genitive plural odnošenij after produkt when the operands are not already named; the short form relativny produkt is permitted locally. - **Kirilična forma:** `релативны продукт одношениј` - **Argumentacija / rationale:** Direct relation component and transparent international modifiers, but conventions differ on relative product versus composition. The English definition at OL-REL-OPERATIONS lines 25-27 fixes the intended sense; this revision selects an edition term without asserting official or native certification. - **Uvěrjenost / status:** 0.6 (medium); `provisional`; revision `OLISV-T0044-r0001`. - **Slovjanske sravnenja / comparanda:** ru: относительное произведение отношений; uk: відносний добуток відношень; pl: iloczyn względny relacji; cs: relativní součin relací; bcs: relativni produkt relacija; bg: относително произведение на отношения. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[14174]; dictionary_id=1992); ISV-GRAMMAR-ADJ (lines 14-18); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** kompozicija odnošenij: Composition is a related convention with possible operand-order ambiguity; the source explicitly names relative product. - **Neizvěstnost / uncertainty:** Terminological and operand-order conventions vary across the literature, and no exact official Interslavic entry was found.; Cross-Slavic specialist surfaces are editorial comparanda from the bounded evidence review and are not represented as official or native-certified forms. ## OLISV-T0039 · relation.strict-order - **English lemma / sense:** strict order — A relation that is irreflexive, asymmetric, and transitive. - **Medžuslovjansky:** `strogy poredok`; lemma `strogy poredok`; noun phrase. - **Upotrěbljenje / inflection:** Masculine adjective agrees with poredok; use strogy linearny poredok for the connected subtype. - **Kirilična forma:** `строгы поредок` - **Argumentacija / rationale:** Inherited poredok component with East and South Slavic support for a strictness stem; West Slavic comparanda diverge. The English definition at OL-REL-ORDERS lines 82-85 fixes the intended sense; this revision selects an edition term without asserting official or native certification. - **Uvěrjenost / status:** 0.65 (medium); `provisional`; revision `OLISV-T0039-r0001`. - **Slovjanske sravnenja / comparanda:** ru: строгий порядок; uk: строгий порядок; pl: porządek ostry; cs: ostré uspořádání; bcs: strogo uređenje; bg: строга наредба. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** ostry poredok: Ostry aligns with Polish and Czech but strogy is clearer across East and South Slavic and already selected in the edition. - **Neizvěstnost / uncertainty:** The specialist phrase is editorial and comparison languages divide between strict and sharp stems.; Cross-Slavic specialist surfaces are editorial comparanda from the bounded evidence review and are not represented as official or native-certified forms. ## OLISV-T0203 · relation.successor - **English lemma / sense:** successor relation — The binary arithmetic relation R in which Rnm holds when m is the immediate successor of n. - **Medžuslovjansky:** `odnošenje naslědnika`; lemma `odnošenje naslědnika`; neuter noun phrase with genitive singular. - **Upotrěbljenje / inflection:** Neuter head with genitive naslědnika; distinguish the binary relation from the canonical successor function. - **Kirilična forma:** `одношење наслєдника` - **Argumentacija / rationale:** The compound extends the already canonical successor-function family and is established in the accepted relation-operations unit. The general dictionary successor row supplies the lexical bridge while the formal source fixes immediacy and argument order. - **Uvěrjenost / status:** 0.86 (high); `provisional`; revision `OLISV-T0203-r0001`. - **Slovjanske sravnenja / comparanda:** ru: отношение непосредственного следования; uk: відношення наступника; pl: relacja następnika; cs: relace následníka; bcs: relacija sljedbenika ili nasljednika; релација следбеника; bg: отношение на непосредствено следване. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[14174]; dictionary_id=1992; lemma=odnošeńje; gloss=relation); ISV-DICT-LIVE-20260825 (wordList[16538]; dictionary_id=9462; lemma=naslědnik; gloss=successor); OL-REL-OPERATIONS-ISV (lines 34-51); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** odnošenje nastupnika: The alternative is understandable but conflicts with the established lane term and would split the successor relation from the canonical successor-function family. - **Neizvěstnost / uncertainty:** The frozen naslědnik row is general-language rather than mathematical; the formal source and accepted relation unit establish the specialist sense. ## OLISV-T0028 · relation.symmetric - **English lemma / sense:** symmetric relation — A relation R for which Rxy implies Ryx. - **Medžuslovjansky:** `simetrično odnošenje`; lemma `simetrično odnošenje`; noun phrase. - **Upotrěbljenje / inflection:** Neuter adjective agrees with odnošenje; use simetrično odnošenje and decline the noun regularly. - **Kirilična forma:** `симетрично одношење` - **Argumentacija / rationale:** Direct relation lemma, regular adjective morphology, inherited mathematical uses of simetričny, and broad comparanda. The English definition at OL-REL-PROPERTIES lines 33-36 fixes the intended sense; this revision selects an edition term without asserting official or native certification. - **Uvěrjenost / status:** 0.73 (medium); `provisional`; revision `OLISV-T0028-r0001`. - **Slovjanske sravnenja / comparanda:** ru: симметричное отношение; uk: симетричне відношення; pl: relacja symetryczna; cs: symetrická relace; bcs: simetrična relacija; bg: симетрично отношение. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[14174]; dictionary_id=1992); ISV-GRAMMAR-ADJ (lines 14-18); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** soglasno odnošenje: The descriptive alternative does not isolate symmetry and is less recognizable as the established mathematical property. - **Neizvěstnost / uncertainty:** No bounded official row attests simetrično odnošenje as a complete term.; Cross-Slavic specialist surfaces are editorial comparanda from the bounded evidence review and are not represented as official or native-certified forms. ## OLISV-T0215 · relation.total - **English lemma / sense:** total relation — A relation on X and Y that relates every x in X to at least one y in Y; here, the existence clause in a graph representation of a function. - **Medžuslovjansky:** `totalno odnošenje`; lemma `totalno odnošenje`; neuter adjective-noun phrase. - **Upotrěbljenje / inflection:** Neuter adjective-noun agreement; genitive totalnogo odnošenja and plural totalna odnošenja. - **Kirilična forma:** `тотално одношење` - **Argumentacija / rationale:** The international adjective is shared or immediately recognizable across all six traditions; the source's quantified clause fixes the precise domain-total sense. - **Uvěrjenost / status:** 0.88 (high); `provisional`; revision `OLISV-T0215-r0001`. - **Slovjanske sravnenja / comparanda:** ru: тотальное отношение; всюду определённое отношение; uk: тотальне відношення; pl: relacja totalna; cs: totální relace; bcs: totalna relacija; bg: тотално отношение. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[17478]; dictionary_id=32744; lemma=totaľny; gloss=total); ISV-DICT-LIVE-20260825 (wordList[14174]; dictionary_id=1992; lemma=odnošeńje; gloss=relation); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** vsegdě opreděljeno odnošenje: The descriptive East-Slavic-style phrase is accurate but longer and less evenly represented across West and South Slavic terminology than the shared international adjective. - **Neizvěstnost / uncertainty:** Total can have different arity-relative readings; this entry is limited to totality on the stated first-coordinate domain X. ## OLISV-T0027 · relation.transitive - **English lemma / sense:** transitive relation — A relation R for which Rxy and Ryz together imply Rxz. - **Medžuslovjansky:** `tranzitivno odnošenje`; lemma `tranzitivno odnošenje`; noun phrase. - **Upotrěbljenje / inflection:** Neuter adjective agrees with odnošenje; use tranzitivno odnošenje and decline the noun regularly. - **Kirilična forma:** `транзитивно одношење` - **Argumentacija / rationale:** Direct relation lemma, official adjective grammar, and inherited adjacent mathematical use of tranzitivny. The English definition at OL-REL-PROPERTIES lines 28-31 fixes the intended sense; this revision selects an edition term without asserting official or native certification. - **Uvěrjenost / status:** 0.76 (high); `provisional`; revision `OLISV-T0027-r0001`. - **Slovjanske sravnenja / comparanda:** ru: транзитивное отношение; uk: транзитивне відношення; pl: relacja przechodnia; cs: tranzitivní relace; bcs: tranzitivna relacija; bg: транзитивно отношение. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[14174]; dictionary_id=1992); ISV-GRAMMAR-ADJ (lines 14-18); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** prěhodno odnošenje: The native-style calque is less uniform cross-Slavically and lacks the inherited mathematical adjective attestation. - **Neizvěstnost / uncertainty:** Inherited evidence attests the adjective in an algebraic-law context, not this exact relation-theoretic compound.; Cross-Slavic specialist surfaces are editorial comparanda from the bounded evidence review and are not represented as official or native-certified forms. ## OLISV-T0045 · relation.transitive-closure - **English lemma / sense:** transitive closure — The least transitive extension represented as the union of all positive powers of a relation. - **Medžuslovjansky:** `tranzitivno zatvorjenje`; lemma `tranzitivno zatvorjenje`; noun phrase. - **Upotrěbljenje / inflection:** Neuter adjective agrees with zatvorjenje; use refleksivno-tranzitivno zatvorjenje for the closure that also adds identity. - **Kirilična forma:** `транзитивно затворјење` - **Argumentacija / rationale:** Inherited adjacent use of tranzitivny plus broad Slavic closure morphology, with a documented East/West versus South lexical split. The English definition at OL-REL-OPERATIONS lines 50-57 fixes the intended sense; this revision selects an edition term without asserting official or native certification. - **Uvěrjenost / status:** 0.65 (medium); `provisional`; revision `OLISV-T0045-r0001`. - **Slovjanske sravnenja / comparanda:** ru: транзитивное замыкание; uk: транзитивне замикання; pl: domknięcie przechodnie; cs: tranzitivní uzávěr; bcs: tranzitivno zatvorenje; bg: транзитивно затваряне. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[14174]; dictionary_id=1992); ISV-GRAMMAR-ADJ (lines 14-18); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** tranzitivno zamknjenje: The zamk- family is strong in East/West Slavic, but zatvorjenje is clearer to South Slavic readers and is fixed in the edition. - **Neizvěstnost / uncertainty:** The full specialist compound is editorial; comparison languages diverge on the closure noun.; Cross-Slavic specialist surfaces are editorial comparanda from the bounded evidence review and are not represented as official or native-certified forms. ## OLISV-T0041 · relation.tree - **English lemma / sense:** tree — A partially ordered set with a unique least root and well-ordered predecessor sets. - **Medžuslovjansky:** `drěvo`; lemma `drěvo`; noun. - **Upotrěbljenje / inflection:** Neuter noun; genitive singular drěva, nominative plural drěva. The set-theoretic sense is determined by context. - **Kirilična forma:** `дрєво` - **Argumentacija / rationale:** A highly transparent inherited Slavic noun with broad cognacy, though Czech and BCS choose different everyday roots. The English definition at OL-REL-TREES lines 49-54 fixes the intended sense; this revision selects an edition term without asserting official or native certification. - **Uvěrjenost / status:** 0.67 (medium); `provisional`; revision `OLISV-T0041-r0001`. - **Slovjanske sravnenja / comparanda:** ru: дерево; uk: дерево; pl: drzewo; cs: strom; bcs: stablo; bg: дърво. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** strom: Strom is favored in Czech and Slovak, but drěvo has stronger East, Polish, and Bulgarian cognacy and was selected consistently in the edition. - **Neizvěstnost / uncertainty:** The bounded official evidence does not directly certify drěvo for the set-theoretic specialist sense.; Cross-Slavic specialist surfaces are editorial comparanda from the bounded evidence review and are not represented as official or native-certified forms. ## OLISV-T0248 · relation.well-ordering - **English lemma / sense:** well-ordering — A linear ordering in which every non-empty subset has a least element. - **Medžuslovjansky:** `dobro oporędčeny poredok`; lemma `dobro oporędčeny poredok`; masculine noun phrase. - **Upotrěbljenje / inflection:** Use dobro oporędčeny poredok; genitive dobro oporędčenogo poredka. The target's dobro uporedane is a prose variant. - **Kirilična forma:** `добро опоредчены поредок` - **Argumentacija / rationale:** The pinned dictionary directly supplies oporędčeny, and the source defines the notion by least elements. The canonical head normalizes the target's inflected prose wording without changing the formula. - **Uvěrjenost / status:** 0.86 (high); `provisional`; revision `OLISV-T0248-r0002`. - **Slovjanske sravnenja / comparanda:** ru: хороший порядок; uk: добрий порядок; pl: dobrze uporządkowany porządek; cs: dobré uspořádání; bcs: dobro uređenje; добро уређење; bg: добра наредба. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (dictionary_id=20002; lemma=oporędčeny; gloss=well-ordered); ISV-DICT-LIVE-20260825 (dictionary_id=3145; lemma=porędȯk; gloss=order, sequence); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** linearny poredok: Only states linearity and omits the least-element condition.; dobro uporedane množstvo: Names a well-ordered set rather than the ordering relation/class. - **Neizvěstnost / uncertainty:** The phrase dobro oporędčeny poredok is a transparent editorial normalization, not a single dictionary headword.; The r0001 record remains preserved as adverse provenance for the target/source locator mismatch. ## OLISV-T0165 · semantics.denote - **English lemma / sense:** denote; refer to — For a constant or singular term to have a specified object as its semantic value in a structure; free logic may permit a name not to denote any domain object. - **Medžuslovjansky:** `označati`; lemma `označati`; transitive imperfective verb. - **Upotrěbljenje / inflection:** Use označati objekt for the ongoing or generic semantic relation; context must distinguish denote from appoint, designate, or imply. The corresponding perfective selection is not fixed here. - **Kirilična forma:** `означати` - **Argumentacija / rationale:** The frozen dictionary directly glosses označati with denote and provides comparison columns across the six traditions. The source fixes the model-theoretic sense and contrasts denoting a domain object with failure to refer. - **Uvěrjenost / status:** 0.94 (high); `provisional`; revision `OLISV-T0165-r0001`. - **Slovjanske sravnenja / comparanda:** ru: обозначать, означать, подразумевать; uk: позначати, позначувати; pl: wyznaczać; cs: jmenovat, určovat, označovat, naznačovat,; bcs: određivati, utvrđivati, ustanovljivati, imenovati; одређивати, именовати; bg: знача, означавам, назначавам. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-DICT-LIVE-20260825 (wordList[996]; dictionary_id=1069); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** navęzyvati na: The frozen refer family is oriented toward citation or reference-to material and is less exact for a term's semantic value. - **Neizvěstnost / uncertainty:** The direct lemma is polysemous outside model theory; formal context supplies the denotation boundary. ## OLISV-T0211 · set-theory.axiom-choice - **English lemma / sense:** axiom of choice — The choice axiom named as the C in ZFC; no particular equivalent formulation is selected in this unit. - **Medžuslovjansky:** `aksioma izbora`; lemma `aksioma izbora`; feminine noun phrase with genitive singular. - **Upotrěbljenje / inflection:** Feminine head aksioma with genitive singular izbora; instrumental s aksiomoju izbora. - **Kirilična forma:** `аксиома избора` - **Argumentacija / rationale:** The compact genitive compound is structurally shared across the comparison languages and composes two directly registered heads. - **Uvěrjenost / status:** 0.98 (high); `provisional`; revision `OLISV-T0211-r0001`. - **Slovjanske sravnenja / comparanda:** ru: аксиома выбора; uk: аксіома вибору; pl: aksjomat wyboru; cs: axiom výběru; bcs: aksiom izbora; bg: аксиома на избора. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[1498]; dictionary_id=24180; lemma=aksioma; gloss=axiom); ISV-DICT-LIVE-20260825 (wordList[3311]; dictionary_id=4333; lemma=izbor; gloss=choice); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** aksioma vybera: The vyber family is regionally transparent, but izbor is the registered Interslavic head and matches the established South Slavic axiom phrase without impairing East or West Slavic recognition. - **Neizvěstnost / uncertainty:** This entry names the axiom only; equivalent formulations and their proof-theoretic dependencies remain outside this source unit. ## OLISV-T0209 · set-theory.discipline - **English lemma / sense:** set theory — The mathematical discipline and first-order axiomatic framework whose basic objects are sets and whose primitive relation here is membership. - **Medžuslovjansky:** `teorija množstv`; lemma `teorija množstv`; feminine noun phrase with genitive plural. - **Upotrěbljenje / inflection:** Feminine head; genitive teorije množstv and locative v teoriji množstv. The complement množstv remains genitive plural. - **Kirilična forma:** `теорија множств` - **Argumentacija / rationale:** The genitive construction is immediately transparent across East, West, and South Slavic terminology and reuses the existing mathematical-set canon instead of importing a narrower national synonym. - **Uvěrjenost / status:** 0.98 (high); `provisional`; revision `OLISV-T0209-r0001`. - **Slovjanske sravnenja / comparanda:** ru: теория множеств; uk: теорія множин; pl: teoria mnogości; cs: teorie množin; bcs: teorija skupova; bg: теория на множествата. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[17168]; dictionary_id=4739; lemma=teorija; gloss=theory); ISV-DICT-LIVE-20260825 (wordList[15156]; dictionary_id=36434; lemma=množstvo; gloss=set (mathematics)); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** teorija skupov: Skup is prominent in part of South Slavic usage, but množstvo is the established lane-wide mathematical-set head and aligns more broadly with the East and West Slavic comparison set. - **Neizvěstnost / uncertainty:** National languages divide between množina/mnogość and skup families; the canon deliberately privileges continuity with the lane's existing množstvo head. ## OLISV-T0210 · set-theory.zfc - **English lemma / sense:** Zermelo--Fraenkel set theory with the axiom of choice — The ZFC axiom system as named in the source, without any claim that it is complete, uniquely foundational, or absolutely consistent. - **Medžuslovjansky:** `teorija množstv Zermela--Fraenkela s aksiomoju izbora`; lemma `teorija množstv Zermela--Fraenkela s aksiomoju izbora`; proper-name noun phrase. - **Upotrěbljenje / inflection:** The theory head declines normally; Zermela and Fraenkela are genitive proper-name complements, while s governs instrumental aksiomoju. - **Kirilična forma:** `теорија множств Зермела--Фраенкела с аксиомоју избора` - **Argumentacija / rationale:** The full form makes the acronym usable without English and preserves the source's proper names and the explicit choice-axiom qualifier. A genitive proper-name construction avoids choosing one national possessive pattern over the others. - **Uvěrjenost / status:** 0.95 (high); `provisional`; revision `OLISV-T0210-r0001`. - **Slovjanske sravnenja / comparanda:** ru: теория множеств Цермело—Френкеля с аксиомой выбора; uk: теорія множин Цермело—Френкеля з аксіомою вибору; pl: teoria mnogości Zermela–Fraenkla z aksjomatem wyboru; cs: Zermelova–Fraenkelova teorie množin s axiomem výběru; bcs: Zermelo–Fraenkelova teorija skupova s aksiomom izbora; bg: теория на множествата на Цермело–Френкел с аксиомата на избора. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[17168,15156]; dictionary_id=4739,36434; lemma=teorija,množstvo); ISV-DICT-LIVE-20260825 (wordList[1498,3311]; dictionary_id=24180,4333; lemma=aksioma,izbor); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** Zermelo--Fraenkelova teorija množstv s aksiomom izbora: The adjectival alternative is understandable but mixes an indeclinable first name with a possessive second name; the selected parallel genitives are more regular in the lane's controlled prose. - **Neizvěstnost / uncertainty:** The source's statement that ZFC proves almost everything mathematicians expect is heuristic; this entry does not endorse completeness, uniqueness, or an absolute consistency claim. ## OLISV-T0217 · set.cantor-theorem - **English lemma / sense:** Cantor's theorem — The theorem instantiated here as the nonexistence of an injection from the power set of X into X. - **Medžuslovjansky:** `Kantorova teorema`; lemma `Kantorova teorema`; feminine proper-name possessive phrase. - **Upotrěbljenje / inflection:** Feminine adjective-noun agreement; genitive Kantorovoj teoremy. Keep initial K in both scripts. - **Kirilična forma:** `Канторова теорема` - **Argumentacija / rationale:** Kantorova preserves the internationally recognized name while ensuring deterministic Cyrillic yields Канторова. The accepted predecessor spells the Latin head Cantorova; this continuation deliberately normalizes only its initial letter for script stability while retaining the same no-injection sense. - **Uvěrjenost / status:** 0.94 (high); `provisional`; revision `OLISV-T0217-r0001`. - **Slovjanske sravnenja / comparanda:** ru: теорема Кантора; uk: теорема Кантора; pl: twierdzenie Cantora; cs: Cantorova věta; bcs: Cantorov teorem; bg: теорема на Кантор. - **Dokazy / evidence:** OL-SIZE-COMPARING-ISV (lines 11, 58-59, 147-153); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** Cantorova teorema: Latin C would deterministically project to Cyrillic Ц, producing the misleading form Цанторова; the canonical K spelling is script-stable and matches East and Bulgarian usage. - **Neizvěstnost / uncertainty:** Polish, Czech, and BCS conventionally retain Latin C; the K spelling is a deliberate bilingual-script normalization, not a claim that those national spellings are wrong. ## OLISV-T0214 · set.cartesian-product - **English lemma / sense:** Cartesian product — The set of ordered pairs whose first coordinate belongs to X and second coordinate belongs to Y. - **Medžuslovjansky:** `kartezijansky produkt`; lemma `kartezijansky produkt`; masculine adjective-noun phrase. - **Upotrěbljenje / inflection:** Masculine adjective-noun agreement; genitive kartezijanskogo produkta and plural kartezijanske produkty. - **Kirilična forma:** `картезијанскы продукт` - **Argumentacija / rationale:** The accepted term combines the internationally recognizable Cartesian stem with produkt, which aligns especially well with Polish, Czech, and BCS practice while the displayed definition removes any algebraic ambiguity. - **Uvěrjenost / status:** 0.92 (high); `provisional`; revision `OLISV-T0214-r0001`. - **Slovjanske sravnenja / comparanda:** ru: декартово произведение; uk: декартів добуток; pl: iloczyn kartezjański; cs: kartézský součin; bcs: Kartezijev produkt; bg: декартово произведение. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[13491]; dictionary_id=5328; lemma=produkt; gloss=product); OL-SET-PAIRS-PRODUCTS-ISV (lines 39-64); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** dekartovo proizvedenje: The East/Bulgarian calque is recognizable but less even across the six comparison traditions and conflicts with the already accepted project head. - **Neizvěstnost / uncertainty:** National traditions divide between Descartes-based calques and Cartesian internationalisms; the accepted project precedent resolves the editorial choice. ## OLISV-T0208 · set.cofinite-subset - **English lemma / sense:** co-finite subset — A subset whose complement in the ambient domain is finite. - **Medžuslovjansky:** `podmnožstvo s konečnym dopolnjenjem`; lemma `podmnožstvo s konečnym dopolnjenjem`; neuter descriptive noun phrase. - **Upotrěbljenje / inflection:** Neuter head; genitive podmnožstva s konečnym dopolnjenjem and plural podmnožstva s konečnym dopolnjenjem. - **Kirilična forma:** `подмножство с конечным дополњењем` - **Argumentacija / rationale:** The descriptive phrase exposes the defining finite-complement property to readers across Slavic traditions instead of making comprehension depend on the compact international prefix co-. It reuses the established finite-set family. - **Uvěrjenost / status:** 0.95 (high); `provisional`; revision `OLISV-T0208-r0001`. - **Slovjanske sravnenja / comparanda:** ru: кофинитное подмножество; подмножество с конечным дополнением; uk: кофінітна підмножина; підмножина зі скінченним доповненням; pl: podzbiór koskończony; podzbiór o skończonym dopełnieniu; cs: kofinitní podmnožina; podmnožina s konečným doplňkem; bcs: kofinitan podskup; podskup s konačnim komplementom; кофинитан подскуп; bg: кофинитно подмножество; подмножество с крайно допълнение. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[16499]; dictionary_id=36456; lemma=podmnožstvo; gloss=subset (mathematics)); ISV-DICT-LIVE-20260825 (wordList[3800]; dictionary_id=7205; lemma=dopȯlnjeńje; gloss=complement); ISV-DICT-LIVE-20260825 (wordList[6943]; dictionary_id=17676; lemma=konėčnosť; gloss=finiteness, finality); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** kofinitno podmnožstvo: The compact internationalism is useful as an alias but is less immediately parsable across the intended broad readership than the explicit finite-complement phrase. - **Neizvěstnost / uncertainty:** The descriptive phrase is intentionally longer than the specialist internationalism kofinitny; the latter remains a documented comparison form rather than the primary head. ## OLISV-T0067 · set.denumerable - **English lemma / sense:** denumerable set — A set in bijection with the natural numbers; equivalently, a countably infinite set. - **Medžuslovjansky:** `izčisljivo bezkonečno množstvo`; lemma `izčisljivo bezkonečno množstvo`; neuter noun phrase. - **Upotrěbljenje / inflection:** Izčisljivo is an invariant adverb modifying bezkonečny; inflect bezkonečny with the head noun, giving neuter singular izčisljivo bezkonečno množstvo. - **Kirilična forma:** `изчисљиво безконечно множство` - **Argumentacija / rationale:** The inherited mathematical corpus directly supplies izčisljivo plus an infinite adjective in the countably infinite sense; the edition normalizes beskonečny to dictionary-backed standard basic bezkonečny while preserving the substantive distinction from computability. - **Uvěrjenost / status:** 0.8 (high); `provisional`; revision `OLISV-T0067-r0001`. - **Slovjanske sravnenja / comparanda:** ru: счётно-бесконечное множество; uk: зліченно-нескінченна множина; pl: zbiór przeliczalnie nieskończony; cs: spočetně nekonečná množina; bcs: prebrojivo beskonačan skup; bg: изброимо безкрайно множество. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[2804]; dictionary_id=5879; lemma=izčisliti); ISV-DICT-LIVE-20260825 (wordList[6136]; dictionary_id=6520; lemma=bezkonėčny); ISV-DICT-LIVE-20260825 (wordList[15156]; dictionary_id=36434; lemma=množstvo; gloss=set (mathematics)); ISV-GRAMMAR-ADJ (lines 49-51); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** sčisljivo bezkonečno množstvo: The sčisl- base is transparently tied to counting but lacks the exact inherited mathematical phrase attested with izčisljivo.; izčislimo bezkonečno množstvo: The -imy form belongs to the canonical computability term and risks meaning computably infinite rather than countably infinite. - **Neizvěstnost / uncertainty:** The frozen dictionary does not directly list izčisljivy or the complete phrase.; All six national specialist phrases are editorial compositions from exact catalogued components rather than direct specialist-dictionary rows. ## OLISV-T0002 · set.element - **English lemma / sense:** element — An object that belongs to a set. - **Medžuslovjansky:** `element`; lemma `element`; masculine noun. - **Upotrěbljenje / inflection:** Masculine noun; genitive singular elementa, nominative plural elementy. Use x jest elementom množstva A when prose is preferable to x ∈ A. - **Kirilična forma:** `елемент` - **Argumentacija / rationale:** The international lemma has a direct dictionary entry with exceptionally broad comparison-language agreement and is already established throughout the inherited mathematical corpus. - **Uvěrjenost / status:** 0.99 (high); `seed_preferred`; revision `OLISV-T0002-r0001`. - **Slovjanske sravnenja / comparanda:** ru: элемент; uk: елемент; pl: element; cs: prvek, element; bcs: element; bg: елемент. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[6006]; dictionary_id=17372); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** pŕvěstȯk: The alternate dictionary lemma is markedly less intelligible and carries a chemical-element association in its comparison data. - **Neizvěstnost / uncertainty:** No specific uncertainty beyond the provisional edition boundary. ## OLISV-T0190 · set.empty - **English lemma / sense:** empty set — The unique set having no elements, denoted by the empty-set symbol. - **Medžuslovjansky:** `prazdno množstvo`; lemma `prazdno množstvo`; neuter noun phrase. - **Upotrěbljenje / inflection:** The neuter adjective agrees with množstvo: genitive prazdnogo množstva; plural prazdna množstva. - **Kirilična forma:** `праздно множство` - **Argumentacija / rationale:** The two directly frozen components produce a transparent mathematical compound. Prazdno preserves the familiar West/South/Bulgarian root while the comparison table records East-Slavic pust-/porozhn- competition. - **Uvěrjenost / status:** 0.86 (high); `provisional`; revision `OLISV-T0190-r0001`. - **Slovjanske sravnenja / comparanda:** ru: пустое множество; uk: порожня множина; pl: zbiór pusty; cs: prázdná množina; bcs: prazan skup; празан скуп; bg: празно множество. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[6101]; dictionary_id=16335; lemma=pråzdny; gloss=empty); ISV-DICT-LIVE-20260825 (wordList[15156]; dictionary_id=36434; lemma=množstvo; gloss=set (mathematics)); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** pusto množstvo: Pusty is also directly attested and especially transparent in East and West Slavic, but prazdny has broader support for the selected mathematical compound and matches the accepted edition surface. - **Neizvěstnost / uncertainty:** National languages divide between prazd-/pust-/porozhn- roots; the selected form is a project bridge rather than a claim of universal specialist usage. ## OLISV-T0066 · set.enumerable - **English lemma / sense:** enumerable set — A set that is finite or in bijection with the natural numbers; countable in the inclusive sense. - **Medžuslovjansky:** `izčisljivo množstvo`; lemma `izčisljivo množstvo`; neuter noun phrase. - **Upotrěbljenje / inflection:** The derived adjective izčisljivy agrees regularly; use neuter singular izčisljivo with množstvo and plural izčisljive with plural heads. - **Kirilična forma:** `изчисљиво множство` - **Argumentacija / rationale:** Izčisljivo extends the exact inherited mathematical surface izčisljivo beskonečny to the finite-inclusive superordinate, while -ljiv- keeps countability visibly distinct from canonical izčislimy meaning computable. - **Uvěrjenost / status:** 0.68 (medium); `provisional`; revision `OLISV-T0066-r0001`. - **Slovjanske sravnenja / comparanda:** ru: счётное множество; uk: зліченна множина; pl: zbiór przeliczalny; cs: spočetná množina; bcs: prebrojiv skup; bg: изброимо множество. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[2804]; dictionary_id=5879; lemma=izčisliti); ISV-DICT-LIVE-20260825 (wordList[15156]; dictionary_id=36434; lemma=množstvo; gloss=set (mathematics)); ISV-GRAMMAR-ADJ (lines 14-18 and 49-51); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** izčislimo množstvo: This is surface-identical to the neuter form of canonical izčislimy and would collapse countability into computability.; sčisljivo množstvo: The sčisl- base is transparently connected with counting but lacks the exact inherited specialist occurrence supplied for izčisljivo. - **Neizvěstnost / uncertainty:** The adjective izčisljivy is reconstructed from the inherited surface izčisljivo rather than directly listed in the frozen dictionary.; National specialist comparanda are editorial derivations from catalogued components, and finite-inclusivity conventions are not uniform. ## OLISV-T0251 · set.even-cardinality - **English lemma / sense:** even cardinality — Having a finite number of elements divisible by two. - **Medžuslovjansky:** `parna velikost`; lemma `parna velikost`; feminine adjective-noun phrase. - **Upotrěbljenje / inflection:** Genitive parnoj velikosti; use čislo parno and parna velikost množstva according to scope. - **Kirilična forma:** `парна великост` - **Argumentacija / rationale:** The source deliberately leaves this as an exercise; the canon records a usable name without pretending the exercise has been solved. Parna is directly pinned, while velikost preserves the edition's established size vocabulary. - **Uvěrjenost / status:** 0.76 (high); `provisional`; revision `OLISV-T0251-r0002`. - **Slovjanske sravnenja / comparanda:** ru: чётная мощность; uk: парна потужність; pl: parzysta moc; cs: sudá mohutnost; bcs: parna kardinalnost; парна кардиналност; bg: четна мощност. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (dictionary_id=29861; lemma=parny; gloss=even); ISV-DICT-LIVE-20260825 (dictionary_id=17215; lemma=čislo; gloss=number); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** parno čislo: Names an even integer, not the cardinality of a domain.; parna kardinalnost: Internationally precise but less transparent to readers who know only the basic size vocabulary. - **Neizvěstnost / uncertainty:** The term cardinality has competing national roots; the target intentionally uses the accessible size phrasing.; The r0001 record remains preserved as adverse provenance for the target/source locator mismatch. ## OLISV-T0193 · set.extensionality - **English lemma / sense:** set extensionality — The principle that sets with exactly the same elements are equal. - **Medžuslovjansky:** `ekstensionalnost množstv`; lemma `ekstensionalnost množstv`; feminine noun phrase with genitive plural. - **Upotrěbljenje / inflection:** Feminine head; genitive ekstensionalnosti množstv. The corresponding axiom may be called aksioma ekstensionalnosti. - **Kirilična forma:** `екстенсионалност множств` - **Argumentacija / rationale:** The qualified head preserves the edition's established s-normalized extensionality family while separating equality-by-membership for sets from OLISV-T0173's semantic invariance principle for formulas and structures. - **Uvěrjenost / status:** 0.81 (high); `provisional`; revision `OLISV-T0193-r0001`. - **Slovjanske sravnenja / comparanda:** ru: экстенсиональность множеств; uk: екстенсіональність множин; pl: ekstensjonalność zbiorów; cs: extenzionalita množin; bcs: ekstenzionalnost skupova; екстензионалност скупова; bg: екстензионалност на множествата. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[6583]; dictionary_id=37683; lemma=ekstensivny; gloss=extensive); ISV-DICT-LIVE-20260825 (wordList[15156]; dictionary_id=36434; lemma=množstvo; gloss=set (mathematics)); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** ekstensionalnost: The short form is valid in a clearly set-theoretic context, but the canonical head needs a qualifier to prevent collision with the distinct logical-extensionality entry. - **Neizvěstnost / uncertainty:** No exact set-extensionality lemma occurs in the frozen dictionary.; National spellings divide between s and z; the project retains its established s-normalization. ## OLISV-T0086 · set.finite - **English lemma / sense:** finite set; finite domain — A set or structure domain containing only finitely many elements. - **Medžuslovjansky:** `konečno množstvo`; lemma `konečno množstvo`; neuter noun phrase. - **Upotrěbljenje / inflection:** Use konečny with masculine domen, konečna with struktura, and konečno with množstvo. - **Kirilična forma:** `конечно множство` - **Argumentacija / rationale:** The direct finiteness noun and mathematical-set head support the edition's stable konečny family, with agreement recorded for set, domain, and structure. - **Uvěrjenost / status:** 0.88 (high); `provisional`; revision `OLISV-T0086-r0001`. - **Slovjanske sravnenja / comparanda:** ru: конечное множество; uk: скінченна множина; pl: zbiór skończony; cs: konečná množina; bcs: konačan skup; bg: крайно множество. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[6943], wordList[15156]; dictionary_id=17676,36434); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** finitno množstvo: The frozen finitny adjective is explicitly restricted to finite verbs.; ograničeno množstvo: Bounded or limited does not imply finitely many elements. - **Neizvěstnost / uncertainty:** The ordinary konečny row also carries final/end meanings; formal context fixes finiteness. ## OLISV-T0161 · set.hereditarily-finite - **English lemma / sense:** hereditarily finite set — A set all of whose members, their members, and so on through the transitive membership ancestry are finite; the displayed HF structure is generated by iterated power sets from the empty set. - **Medžuslovjansky:** `naslědstveno konečno množstvo`; lemma `naslědstveno konečno množstvo`; neuter noun phrase. - **Upotrěbljenje / inflection:** Naslědstveno is an invariant adverb modifying konečno; inflect konečny with the neuter head množstvo. Use the plural naslědstveno konečna množstva. - **Kirilična forma:** `наслєдствено конечно множство` - **Argumentacija / rationale:** The term composes the directly registered inheritance family and mathematical-set head with the already canonical finite-set family. Its structure tracks the dominant Russian and South-Slavic specialist phrase while remaining legible beside West-Slavic hereditary or inherited-root variants. - **Uvěrjenost / status:** 0.74 (medium); `provisional`; revision `OLISV-T0161-r0001`. - **Slovjanske sravnenja / comparanda:** ru: наследственно конечное множество; uk: спадково скінченна множина; pl: zbiór dziedzicznie skończony; cs: dědičně konečná množina; bcs: nasljedno konačan skup; наследно коначан скуп; bg: наследствено крайно множество. - **Dokazy / evidence:** ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-DICT-LIVE-20260825 (wordList[8441]; dictionary_id=761); ISV-DICT-LIVE-20260825 (wordList[6943]; dictionary_id=17676); ISV-DICT-LIVE-20260825 (wordList[15156]; dictionary_id=36434); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** naslědno finitno množstvo: Finitny in the frozen dictionary is restricted to finite verbs, while naslědno does not express closure through the complete membership ancestry as clearly.; dědično konečno množstvo: West-Slavic readers may find the dědič- family more immediate, but it is less transparent across East and South Slavic traditions than the directly registered naslěd- family. - **Neizvěstnost / uncertainty:** The complete Interslavic compound is editorial rather than a direct dictionary lemma.; Bulgarian commonly uses krajno rather than the konečny family for mathematical finiteness.; The short source gloss is sharpened by its displayed cumulative hierarchy rather than by a standalone prose definition. ## OLISV-T0087 · set.infinite - **English lemma / sense:** infinite set; infinite domain — A set or structure domain that is not finite and therefore has infinitely many elements. - **Medžuslovjansky:** `bezkonečno množstvo`; lemma `bezkonečno množstvo`; neuter noun phrase. - **Upotrěbljenje / inflection:** Use bezkonečny with masculine domen, bezkonečna with struktura, and bezkonečno with množstvo. - **Kirilična forma:** `безконечно множство` - **Argumentacija / rationale:** The direct infinite adjective is already stable in accepted mathematical prose, and the mathematical-set head yields an exact phrase. - **Uvěrjenost / status:** 0.93 (high); `provisional`; revision `OLISV-T0087-r0001`. - **Slovjanske sravnenja / comparanda:** ru: бесконечное множество; uk: нескінченна множина; pl: zbiór nieskończony; cs: nekonečná množina; bcs: beskonačan skup; bg: безкрайно множество; безконечно множество. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[6136], wordList[15156]; dictionary_id=6520,36434); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** nekonečno množstvo: A strong West/Ukrainian-style alternative, but the frozen Interslavic head directly selects bezkonečny. - **Neizvěstnost / uncertainty:** West Slavic and Ukrainian forms prefer ne- rather than bez-. ## OLISV-T0005 · set.intersection - **English lemma / sense:** intersection — The set containing exactly the elements common to all operand sets. - **Medžuslovjansky:** `prěsěčenje množstv`; lemma `prěsěčenje`; neuter noun phrase. - **Upotrěbljenje / inflection:** The dictionary source form prěsěčeńje is normalized to standard/basic prěsěčenje. The head is neuter; use prěsěčenje množstv A i B or A ∩ B. - **Kirilična forma:** `прєсєчење множств` - **Argumentacija / rationale:** The normalized dictionary lemma is reinforced by an exact mathematical intersection use in the inherited corpus; množstv makes the Open Logic set-theoretic sense explicit. - **Uvěrjenost / status:** 0.91 (high); `seed_preferred`; revision `OLISV-T0005-r0001`. - **Slovjanske sravnenja / comparanda:** ru: пересечение множеств; uk: перетин множин; pl: przecięcie zbiorów; cs: průnik množin; bcs: presjek skupova / presek skupova; bg: сечение на множества. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[9476]; dictionary_id=21469); ISV-DICT-LIVE-20260824 (wordList[15156]; dictionary_id=36434); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** križišče množstv: Križišče is strongly biased toward a physical road intersection and lacks inherited mathematical support. - **Neizvěstnost / uncertainty:** Several comparison languages use a specialist noun different from the general-intersection dictionary column; those domain-normalized comparanda are explicitly marked componential. ## OLISV-T0001 · set.mathematical - **English lemma / sense:** set — A collection treated as one mathematical object. - **Medžuslovjansky:** `množstvo`; lemma `množstvo`; neuter noun. - **Upotrěbljenje / inflection:** Neuter noun; genitive singular množstva, nominative/accusative plural množstva. Use for mathematical sets, including množstvo A. - **Kirilična forma:** `множство` - **Argumentacija / rationale:** The official dictionary row is explicitly mathematical, the form is pan-Slavically legible, and the maintained Noether corpus uses the same lemma in set-like mathematical prose. - **Uvěrjenost / status:** 0.99 (high); `seed_preferred`; revision `OLISV-T0001-r0001`. - **Slovjanske sravnenja / comparanda:** ru: множество; uk: множина; pl: zbiór; cs: množina; bcs: skup; bg: множество. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[15156]; dictionary_id=36434); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** sbirka: The dictionary marks this as a general collection/set, not the mathematical sense, and the mathematical row supplies a dedicated lemma. - **Neizvěstnost / uncertainty:** No specific uncertainty beyond the provisional edition boundary. ## OLISV-T0194 · set.naive-comprehension-schema - **English lemma / sense:** naive comprehension scheme — The unrestricted schema asserting that every condition determines a set of exactly the objects satisfying it, which yields contradiction in the displayed theory. - **Medžuslovjansky:** `naivna shema tvorjenja množstv`; lemma `naivna shema tvorjenja množstv`; feminine noun phrase. - **Upotrěbljenje / inflection:** Feminine head; genitive naivnoj shemy tvorjenja množstv. Use one instance of the schema for one formula. - **Kirilična forma:** `наивна схема творјења множств` - **Argumentacija / rationale:** Naivna shema tvorjenja množstv is built from directly frozen components and is more immediately transparent than an unexplained comprehension internationalism. The canon still records the international alternative for readers coming from Polish, Czech, or Anglophone logic. - **Uvěrjenost / status:** 0.78 (medium); `provisional`; revision `OLISV-T0194-r0001`. - **Slovjanske sravnenja / comparanda:** ru: наивная схема выделения множеств; uk: наївна схема утворення множин; pl: naiwny schemat komprehensji; cs: naivní schéma komprehenze; bcs: naivna shema tvorbe skupova; наивна шема формирања скупова; bg: наивна схема за образуване на множества. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[11502]; dictionary_id=16721; lemma=naivny; gloss=naive); ISV-DICT-LIVE-20260825 (wordList[14890]; dictionary_id=18814; lemma=shema; gloss=scheme); ISV-DICT-LIVE-20260825 (wordList[4404]; dictionary_id=3381; lemma=stvorjeńje; gloss=creation); ISV-DICT-LIVE-20260825 (wordList[15156]; dictionary_id=36434; lemma=množstvo; gloss=set (mathematics)); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** naivna shema komprehensije: The international term is exact and strong in some specialist traditions, but it lacks a frozen Interslavic head and is less compositionally transparent to the broad Slavic readership. - **Neizvěstnost / uncertainty:** The source does not state syntactic side conditions on the schema variable A.; National specialist traditions split between native formation/separation phrasing and the international comprehension family. ## OLISV-T0068 · set.nonenumerable - **English lemma / sense:** nonenumerable set — A set that is not enumerable; equivalently, an uncountable set. - **Medžuslovjansky:** `neizčisljivo množstvo`; lemma `neizčisljivo množstvo`; neuter noun phrase. - **Upotrěbljenje / inflection:** Transparent ne- negation of izčisljivy; use neuter singular neizčisljivo with množstvo and inflect the adjective regularly with other heads. - **Kirilična forma:** `неизчисљиво множство` - **Argumentacija / rationale:** Neizčisljivo is the transparent morphological complement of the selected enumerable term and avoids adopting nesčisljeny, whose direct dictionary sense is ordinary countless or innumerable rather than the exact set-theoretic complement. - **Uvěrjenost / status:** 0.64 (medium); `provisional`; revision `OLISV-T0068-r0001`. - **Slovjanske sravnenja / comparanda:** ru: несчётное множество; uk: незліченна множина; pl: zbiór nieprzeliczalny; cs: nespočetná množina; bcs: neprebrojiv skup; bg: неизброимо множество. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[2804]; dictionary_id=5879; lemma=izčisliti); ISV-DICT-LIVE-20260825 (wordList[15156]; dictionary_id=36434; lemma=množstvo; gloss=set (mathematics)); ISV-GRAMMAR-ADJ (lines 14-18 and 49-51); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** nesčisljeno množstvo: The directly attested adjective means countless or innumerable and can function as quantitative hyperbole; it does not precisely negate the selected enumerable predicate.; neizčislimo množstvo: This would negate canonical izčislimy in the computability sense and therefore mean noncomputable rather than nonenumerable. - **Neizvěstnost / uncertainty:** The adjective is an edition-level derivation from inherited izčisljivo, not a direct dictionary lemma.; National specialist comparanda are editorially normalized and not independently certified by the bounded dictionary. ## OLISV-T0213 · set.ordered-pair - **English lemma / sense:** ordered pair — A two-place ordered object represented in this source by the Kuratowski set {{x},{x,y}}; the representation is not claimed to be unique. - **Medžuslovjansky:** `uporędžena para`; lemma `uporędžena para`; feminine noun phrase. - **Upotrěbljenje / inflection:** Feminine adjective-noun agreement; genitive uporędženej pary and plural uporędžene pary. - **Kirilična forma:** `упореджена пара` - **Argumentacija / rationale:** The established lane phrase bridges East Slavic uporyadočen- and West/South Slavic ordered-pair families while retaining the broadly shared para head. - **Uvěrjenost / status:** 0.93 (high); `provisional`; revision `OLISV-T0213-r0001`. - **Slovjanske sravnenja / comparanda:** ru: упорядоченная пара; uk: впорядкована пара; pl: para uporządkowana; cs: uspořádaná dvojice; bcs: uređeni par; bg: наредена двойка. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[4323]; dictionary_id=2257; lemma=para; gloss=pair); OL-SET-PAIRS-PRODUCTS-ISV (lines 10-37); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** uređena para: The South Slavic form is concise but narrower; uporędžena is already the accepted project form and is more directly recognizable to East and West Slavic readers. - **Neizvěstnost / uncertainty:** The displayed Kuratowski encoding is one representation among several; the term denotes the ordered object, not uniquely that encoding. ## OLISV-T0212 · set.power-set - **English lemma / sense:** power set — For a set X, the set whose elements are exactly all subsets of X. - **Medžuslovjansky:** `množstvo vsih podmnožstv`; lemma `množstvo vsih podmnožstv`; neuter descriptive noun phrase. - **Upotrěbljenje / inflection:** Neuter head; the domain follows as a genitive complement, e.g. množstvo vsih podmnožstv množstva X. - **Kirilična forma:** `множство всих подмножств` - **Argumentacija / rationale:** The descriptive head exposes the defining property to readers across Slavic traditions and is already established in an accepted set-theory unit. It avoids making comprehension depend on national potęgowy/potenční or Boolean-set conventions. - **Uvěrjenost / status:** 0.96 (high); `provisional`; revision `OLISV-T0212-r0001`. - **Slovjanske sravnenja / comparanda:** ru: множество всех подмножеств; булеан; uk: множина всіх підмножин; булеан; pl: zbiór potęgowy; cs: potenční množina; bcs: skup svih podskupova; partitivni skup; bg: множество на всички подмножества; булеан. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[15156,16499]; dictionary_id=36434,36456; lemma=množstvo,podmnožstvo); OL-SET-SUBSETS-ISV (lines 79-84); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** potencijalno množstvo: The international adjective follows West Slavic usage but can read as merely potential and is less transparent than the exact all-subsets definition. - **Neizvěstnost / uncertainty:** Bulean and national power/potential adjectives remain useful aliases; the canon selects the maximally transparent descriptive form. ## OLISV-T0247 · set.proper-subset - **English lemma / sense:** proper subset — A subset that is not equal to the set containing it. - **Medžuslovjansky:** `vlastno podmnožstvo`; lemma `vlastno podmnožstvo`; neuter adjective-noun phrase. - **Upotrěbljenje / inflection:** Genitive vlastnogo podmnožstva; use A jest vlastnym podmnožstvom B for the strict inclusion relation. - **Kirilična forma:** `властно подмножство` - **Argumentacija / rationale:** The direct mathematical subset row anchors the head, while vlastno states the strictness required by the source. This keeps the Dedekind criterion distinct from an arbitrary subset. - **Uvěrjenost / status:** 0.88 (high); `provisional`; revision `OLISV-T0247-r0002`. - **Slovjanske sravnenja / comparanda:** ru: собственное подмножество; uk: власна підмножина; pl: podzbiór właściwy; cs: vlastní podmnožina; bcs: pravo podskup; прави подскуп; bg: същинско подмножество. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (dictionary_id=36456; lemma=podmnožstvo; gloss=subset (mathematics)); ISV-ORTHOGRAPHY (standard Latin alphabet and Cyrillic equivalence sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** strogy podmnožstvo: Strogy is already used for strict syntactic subforms and is less idiomatic for set inclusion.; podmnožstvo s konečnym dopolnjenjem: Describes a cofinite subset, not every proper subset. - **Neizvěstnost / uncertainty:** The complete phrase is compositional; national mathematical adjectives vary.; The r0001 record remains preserved as adverse provenance for the target/source locator mismatch. ## OLISV-T0191 · set.pure - **English lemma / sense:** pure set — A set whose elements, recursively, are themselves sets, so that its transitive formation contains no urelements. - **Medžuslovjansky:** `čisto množstvo`; lemma `čisto množstvo`; neuter noun phrase. - **Upotrěbljenje / inflection:** The neuter adjective agrees with množstvo: genitive čistogo množstva; plural čista množstva. - **Kirilična forma:** `чисто множство` - **Argumentacija / rationale:** Čisto množstvo is a direct componential match across the six comparison traditions, and the current source supplies the recursive no-urelement boundary. - **Uvěrjenost / status:** 0.94 (high); `provisional`; revision `OLISV-T0191-r0001`. - **Slovjanske sravnenja / comparanda:** ru: чистое множество; uk: чиста множина; pl: zbiór czysty; cs: čistá množina; bcs: čisti skup; чисти скуп; bg: чисто множество. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[3445]; dictionary_id=582; lemma=čisty; gloss=clean, pure); ISV-DICT-LIVE-20260825 (wordList[15156]; dictionary_id=36434; lemma=množstvo; gloss=set (mathematics)); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** bezurelementno množstvo: The negative compound makes one consequence explicit but is cumbersome and does not express the established recursive pure-set term as directly. - **Neizvěstnost / uncertainty:** The informal source explanation tacitly assumes well-founded formation and does not itself distinguish non-well-founded pure sets. ## OLISV-T0218 · set.russell-paradox - **English lemma / sense:** Russell's paradox — The contradiction produced by unrestricted comprehension applied to the property of not belonging to oneself. - **Medžuslovjansky:** `Russellov paradoks`; lemma `Russellov paradoks`; masculine proper-name possessive phrase. - **Upotrěbljenje / inflection:** Masculine phrase; genitive Russellovogo paradoksa. Preserve the internationally established double l in the proper name. - **Kirilična forma:** `Русселлов парадокс` - **Argumentacija / rationale:** The possessive form is already established in the edition and mirrors Czech/BCS morphology while retaining the proper name recognizable across all comparison languages. - **Uvěrjenost / status:** 0.97 (high); `provisional`; revision `OLISV-T0218-r0001`. - **Slovjanske sravnenja / comparanda:** ru: парадокс Рассела; uk: парадокс Рассела; pl: paradoks Russella; cs: Russellův paradox; bcs: Russellov paradoks; bg: парадокс на Ръсел. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[12428]; dictionary_id=543; lemma=paradoks; gloss=paradox); OL-SET-RUSSELL-ISV (lines 11-80); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** paradoks Russella: The genitive construction is valid and common nationally, but the possessive form is the existing project head and produces a more compact stable label. - **Neizvěstnost / uncertainty:** The paradox depends on unrestricted comprehension; it must not be attributed to the restricted separation schema recorded separately. ## OLISV-T0219 · set.separation-schema - **English lemma / sense:** separation schema — The restricted comprehension schema asserting, for a prior set z and formula A, the existence of the subset of z satisfying A. - **Medžuslovjansky:** `shema vyděljenja`; lemma `shema vyděljenja`; feminine noun phrase with genitive singular. - **Upotrěbljenje / inflection:** Feminine head shema with genitive verbal noun vyděljenja; genitive shemy vyděljenja. - **Kirilična forma:** `схема выдєљења` - **Argumentacija / rationale:** Shema is directly frozen. The selected vyděljenje is an editorial specialist normalization supported by the displayed restricted-comprehension formula and Russian, Ukrainian, and Czech convergence; the frozen odděliti row is adverse generic comparison, not direct support for this stem. Shema records that the displayed form varies with formulas even though the English prose calls it a separation principle. - **Uvěrjenost / status:** 0.86 (high); `provisional`; revision `OLISV-T0219-r0001`. - **Slovjanske sravnenja / comparanda:** ru: схема выделения; uk: схема виділення; pl: schemat aksjomatu wyróżniania; schemat separacji; cs: schéma vydělení; bcs: aksiomska shema separacije; shema izdvajanja; bg: схема на отделянето. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[14890]; dictionary_id=18814; lemma=shema; gloss=scheme); ISV-DICT-LIVE-20260825 (wordList[15104]; dictionary_id=2951; lemma=odděliti; gloss=separate); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** shema separacije: The internationalism is familiar in Polish and BCS specialist usage, but vyděljenje is more directly parsable across the intended audience and better matches the East/West specialist comparison; the frozen generic comparator does not decide between the stems. - **Neizvěstnost / uncertainty:** The English prose calls this the separation principle, whereas the canonical head says schema because the displayed formula is schematic; the source also omits explicit parameter and freshness conditions for A(x), which the canon does not silently supply. ## OLISV-T0003 · set.subset - **English lemma / sense:** subset — A set all of whose elements belong to another set. - **Medžuslovjansky:** `podmnožstvo`; lemma `podmnožstvo`; neuter noun. - **Upotrěbljenje / inflection:** Neuter noun; genitive singular podmnožstva, plural podmnožstva. Use A jest podmnožstvom B for A ⊆ B. - **Kirilična forma:** `подмножство` - **Argumentacija / rationale:** The compound transparently inherits množstvo, is explicitly tagged for mathematics in the dictionary, and occurs with the same sense in the inherited corpus. - **Uvěrjenost / status:** 0.99 (high); `seed_preferred`; revision `OLISV-T0003-r0001`. - **Slovjanske sravnenja / comparanda:** ru: подмножество; uk: підмножина; pl: podzbiór; cs: podmnožina; bcs: podskup; bg: подмножество. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[16499]; dictionary_id=36456); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** podgrupa: A subgroup is only a special kind of subset and cannot serve as the general set-theoretic term. - **Neizvěstnost / uncertainty:** No specific uncertainty beyond the provisional edition boundary. ## OLISV-T0004 · set.union - **English lemma / sense:** union; union over a set — The set containing exactly the elements belonging to at least one member of a specified family; this includes binary union and the operation denoted by union X. - **Medžuslovjansky:** `unija množstv`; lemma `unija`; feminine noun phrase. - **Upotrěbljenje / inflection:** Feminine noun; genitive unije. Use unija množstv for the general operation, unija X or formula notation for the union over a set X, and unija A i B for binary union. - **Kirilična forma:** `унија множств` - **Argumentacija / rationale:** The established international head remains unchanged. OLP-0170 explicitly introduces the family operation union X, so the revision broadens the recorded sense without conflating it with intersection or with the mereological sum introduced later in the same unit. - **Uvěrjenost / status:** 0.72 (medium); `provisional`; revision `OLISV-T0004-r0002`. - **Slovjanske sravnenja / comparanda:** ru: объединение множеств; uk: об'єднання множин; pl: suma zbiorów; cs: sjednocení množin; bcs: unija skupova; bg: обединение на множества. - **Dokazy / evidence:** ISV-DICT-LIVE-20260824 (wordList[18009]; dictionary_id=13296); ISV-DICT-LIVE-20260824 (wordList[15156]; dictionary_id=36434); ISV-ORTHOGRAPHY (standard-alphabet and Cyrillic sections); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** sjedinjenje množstv: This Slavic-rooted alternative is semantically attractive and Noether attests sjedinenje, but no direct noun row or set-union attestation is present in the bounded official snapshot. - **Neizvěstnost / uncertainty:** The choice between unija množstv and sjedinenje množstv needs stronger specialist Interslavic attestation; no human review is required to use this reversible provisional seed. ## OLISV-T0192 · set.urelement - **English lemma / sense:** urelement — An object admitted as an element of sets while not itself being a set. - **Medžuslovjansky:** `urelement`; lemma `urelement`; masculine noun. - **Upotrěbljenje / inflection:** Masculine noun; genitive urelementa, plural urelementy. Use only for a non-set object in a set-theoretic universe. - **Kirilična forma:** `урелемент` - **Argumentacija / rationale:** Urelement is the compact international technical term used by the source and is directly reconstructible from the established element head. Keeping it distinct avoids overloading atom, which has additional logical and mereological senses. - **Uvěrjenost / status:** 0.73 (medium); `provisional`; revision `OLISV-T0192-r0001`. - **Slovjanske sravnenja / comparanda:** ru: урэлемент; uk: урелемент; pl: urelement; cs: urelement; bcs: urelement; урелемент; bg: урелемент. - **Dokazy / evidence:** ISV-DICT-LIVE-20260825 (wordList[6006]; dictionary_id=17372; lemma=element; gloss=element); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; StandardCyrillic type=5, Standard flavorization=3) - **Alternativy / alternatives:** praelement: The calque is morphologically transparent but is not the source term and is less stable across specialist traditions than urelement. - **Neizvěstnost / uncertainty:** No exact urelement entry occurs in the frozen dictionary response.; Atom is deliberately rejected because it is ambiguous across set theory, logic, physics, and mereology. ## OLISV-T0386 · theory.weaker-theory - **English lemma / sense:** weaker theory — A theory with fewer deductive consequences than a comparison theory; in this unit Robinson Q does not prove commutativity of addition and therefore has models excluded by true arithmetic and Peano arithmetic. - **Medžuslovjansky:** `slabša teorija`; lemma `slabša teorija`; feminine comparative adjective-noun phrase. - **Upotrěbljenje / inflection:** Feminine comparative slabša agrees with teorija; use od plus genitive for the comparison, as in slabša od teorije TA. - **Kirilična forma:** `слабша теорија` - **Argumentacija / rationale:** The comparative slabša is already the accepted canon morphology in OLISV-T0268, while the Russian and Croatian sources independently attest the exact theory-strength contrast. The phrase remains relational: it does not mean that Q is absolutely weak for every metamathematical purpose. - **Uvěrjenost / status:** 0.95 (high); `provisional`; revision `OLISV-T0386-r0001`. - **Slovjanske sravnenja / comparanda:** ru: более слабая теория; uk: слабша теорія; pl: słabsza teoria; cs: slabší teorie; bcs: slabija teorija; bg: по-слаба теория. - **Dokazy / evidence:** OL-MODEL-ARITHMETIC-MODELS-Q (lines 13-23); ISV-DICT-LIVE-20260825 (wordList[18597]; dictionary_id=1341; lemma=slaby; gloss=weak, feeble); RU-MI-RAS-PROVABILITY-ARITHMETIC-2020 (physical page 2 / extracted lines 44-52); HR-ZAGREB-GODEL-INCOMPLETENESS-2011 (physical page 2 / extracted lines 96-103); ISV-TRANSLIT-3.4.4 (package/src/transliterate/transliterate.ts; standard Cyrillic, standard flavorization) - **Alternativy / alternatives:** slaba teorija: The positive adjective loses the explicit comparison to TA and PA made in this unit.; malo silna teorija: This analytic phrase is less compact and lacks the official weak-adjective precedent. - **Neizvěstnost / uncertainty:** Theory strength is relative to a comparison theory and proof system; the short phrase relies on the local TA/PA contrast. ## Pravilo reprodukcije · Reproduction rule Replay `CANON_INDEX.json` po porędku, prověri každy byte/hash, grupuj zapisy po `entry_id` i izberi najvyššu nepretrganu aktivnu reviziju. Nikogda ne prěpisuj historiju: dodavaj naslědnik s jasnym supersession, dokazami i neizvěstnostju. Replay `CANON_INDEX.json` in order, verify every byte/hash pin, group by `entry_id`, and select the greatest contiguous active revision. Never overwrite history: append a successor with explicit supersession, evidence and uncertainty. Granica tvrđenja / claim boundary: reverzibilna projektna terminologija, ne oficialna standardizacija, rodnojezyčna certifikacija, naučna recenzija ili dokončenje vsih 722 jedinic.