ASYMPTOTIC TRUTH-VALUE LAWS IN MANY-VALUED LOGICS
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| Název: | ASYMPTOTIC TRUTH-VALUE LAWS IN MANY-VALUED LOGICS |
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| Autoři: | BADIA, GUILLERMO, CAICEDO, XAVIER, NOGUERA, CARLES |
| Přispěvatelé: | Badia, Guillermo, Caicedo, Xavier, Noguera, Carles |
| Zdroj: | The Journal of Symbolic Logic |
| Publication Status: | Preprint |
| Informace o vydavateli: | Cambridge University Press (CUP), 2025. |
| Rok vydání: | 2025 |
| Témata: | many-valued logic, zero-one law, finite distributive lattices with negation, Łukasiewicz predicate logic, FOS: Mathematics, Mathematics - Logic, 16. Peace & justice, Logic (math.LO) |
| Popis: | This paper studies which truth-values are most likely to be taken on finite models by arbitrary sentences of a many-valued predicate logic. The classical zero-one law (independently proved by Fagin and Glebskiĭ et al.) states that every sentence in a purely relational language is almost surely false or almost surely true, meaning that the probability that the formula is true in a randomly chosen finite structures of cardinal n is asymptotically $0$ or $1$ as n grows to infinity. We obtain generalizations of this result for any logic with values in a finite lattice-ordered algebra, and for some infinitely valued logics, including Łukasiewicz logic. The finitely valued case is reduced to the classical one through a uniform translation and Oberschelp’s generalization of the zero-one law. Moreover, it is shown that the complexity of determining the almost sure value of a given sentence is PSPACE-complete (generalizing Grandjean’s result for the classical case), and for some logics we describe completely the set of truth-values that can be taken by sentences almost surely. |
| Druh dokumentu: | Article |
| Popis souboru: | application/pdf; ELETTRONICO |
| Jazyk: | English |
| ISSN: | 1943-5886 0022-4812 |
| DOI: | 10.1017/jsl.2024.46 |
| DOI: | 10.48550/arxiv.2306.13904 |
| Přístupová URL adresa: | http://arxiv.org/abs/2306.13904 https://hdl.handle.net/11365/1287054 https://www.cambridge.org/core/journals/journal-of-symbolic-logic/article/asymptotic-truthvalue-laws-in-manyvalued-logics/2C773BAB9BAB09B525EFE64CE6873DEA https://doi.org/10.1017/jsl.2024.46 |
| Rights: | CC BY arXiv Non-Exclusive Distribution |
| Přístupové číslo: | edsair.doi.dedup.....8e70d0e0a336b48eed42e6c62327ba42 |
| Databáze: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | This paper studies which truth-values are most likely to be taken on finite models by arbitrary sentences of a many-valued predicate logic. The classical zero-one law (independently proved by Fagin and Glebskiĭ et al.) states that every sentence in a purely relational language is almost surely false or almost surely true, meaning that the probability that the formula is true in a randomly chosen finite structures of cardinal n is asymptotically $0$ or $1$ as n grows to infinity. We obtain generalizations of this result for any logic with values in a finite lattice-ordered algebra, and for some infinitely valued logics, including Łukasiewicz logic. The finitely valued case is reduced to the classical one through a uniform translation and Oberschelp’s generalization of the zero-one law. Moreover, it is shown that the complexity of determining the almost sure value of a given sentence is PSPACE-complete (generalizing Grandjean’s result for the classical case), and for some logics we describe completely the set of truth-values that can be taken by sentences almost surely. |
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| ISSN: | 19435886 00224812 |
| DOI: | 10.1017/jsl.2024.46 |