Homotopies in Classical and Paraconsistent Modal Logics

TL;DR

This paper explores topological semantics for classical and paraconsistent modal logics, focusing on transformations between models and measures to track changes, advancing the geometric understanding of these logics.

Contribution

It introduces a framework for transforming topological models in classical and paraconsistent modal logics while preserving validity, and proposes a measure to monitor such transformations.

Findings

Developed methods for model transformations in modal logics

Proposed a measure to track changes in topological models

Extended topological semantics to paraconsistent systems

Abstract

Topological semantics for modal logics has recently gained new momentum in many different branches of logic. In this paper, we will consider the topological semantics of both classical and paraconsistent modal logics. This work is a new step in the research program that focuses on paraconsistent systems from geometric and topological point of view. Here, we discuss the functional transformations in paraconsistent and classical modal cases: how to transform one classical or paraconsistent topological model to another, how to transform one transformation to another in a validity preserving way. Furthermore, we also suggest a measure to keep track of such change.