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arXiv · 2306.13904

Asymptotic truth-value laws in many-valued logics

Guillermo Badia·Xavier Caicedo·Carles Noguera
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Abstract

This paper studies which truth-values are most likely to be taken on finite models by arbitrary sentences of a many-valued predicate logic. We obtain generalizations of Fagin's classical zero-one law 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 Fagin's result. Moreover, it is shown that the complexity of determining the almost sure value of a given sentence is PSPACE-complete, and for some logics we may describe completely the set of truth-values that can be taken by sentences almost surely.

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Guillermo Badia, Xavier Caicedo, Carles Noguera. 2023-09-19. Asymptotic truth-value laws in many-valued logics. https://doi.org/10.1017/jsl.2024.46

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