Strong standard completeness theorems for S5-modal Lukasiewicz logics

2024/08/08 by Diego Castaño, José Patricio Díaz Varela, Castaño, Diego +3 · 1 citation
Computer Science · #Advanced Algebra and Logic #FOS: Mathematics #Formal Methods in Verification #Logic (math.LO) #Logic, Reasoning, and Knowledge

paper · pdf · doi:10.48550/arxiv.2408.04757

openalex publication_date 2024/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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