Homotopies in Classical and Paraconsistent Modal Logics

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.