Asymptotic truth-value laws in many-valued logics
Logic
2026-02-11 v2
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 \L ukasiewicz 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.
Keywords
Cite
@article{arxiv.2306.13904,
title = {Asymptotic truth-value laws in many-valued logics},
author = {Guillermo Badia and Xavier Caicedo and Carles Noguera},
journal= {arXiv preprint arXiv:2306.13904},
year = {2026}
}