Year: 2025
Type: article
Abstract: This paper investigates the extension of lattice-based logics into modal languages.We observe that such extensions admit multiple approaches, as the interpretation of the necessity operator is not uniquely determined by the underlying lattice structure.The most natural interpretation defines necessity as the meet of the truth values of a formula across all accessible worlds-an approach we refer to as the normal interpretation.We examine the logical properties that emerge under this and other interpretations, including the conditions under which the resulting modal logic satisfies the axiom K and other common modal validities.Furthermore, we consider cases in which necessity is attributed exclusively to formulas that hold in all accessible worlds.
DOI: 10.4204/eptcs.430.3
Authors: Alfredo R. Freire, Manuel A. Martins
Institutions: Universidade de Brasília, University of Aveiro
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
Awards: G3069120617, G8175477296
OpenAlex ID: W4414584646
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