Strong standard completeness theorems for S5-modal Lukasiewicz logics
Logic
2024-08-12 v1
Abstract
We study the S5-modal expansion of the logic based on the Lukasiewicz t-norm. We exhibit a finitary propositional calculus and show that it is finitely strongly complete with respect to this logic. This propositional calculus is then expanded with an infinitary rule to achieve strong completeness. These results are derived from properties of monadic MValgebras: functional representations of simple and finitely subdirectly irreducible algebras, as well as the finite embeddability property. We also show similar completeness theorems for the extension of the logic based on models with bounded universe.
Keywords
Cite
@article{arxiv.2408.04757,
title = {Strong standard completeness theorems for S5-modal Lukasiewicz logics},
author = {Diego Castaño and José Patricio Díaz Varela and Gabriel Savoy},
journal= {arXiv preprint arXiv:2408.04757},
year = {2024}
}