Multialgebras and Non-Deterministic Semantics applied to Paraconsistent Logics

TL;DR

This paper advances the theory of multialgebras by redefining free objects and establishing categorical equivalences, while also applying nondeterministic semantics to paraconsistent logics with a novel approach to incompatibility.

Contribution

It introduces a new definition of freely generated objects in multialgebras and demonstrates their categorical equivalence, alongside applying restricted Nmatrices to paraconsistent logics.

Findings

New categorical equivalence between multialgebras and partially ordered algebras

Development of restricted Nmatrices for nondeterministic semantics

Generalization of incompatibility in paraconsistent logics

Abstract

This work is divided between two main areas: in the theory of multialgebras, we focus mostly on a new definition of what a freely generated object should be in their category, and on how this category is equivalent to another with partially ordered algebras as objects; we then use nondeterministic semantics, specially those we have named restricted Nmatrices, on paraconsistent logics and some systems dealing with a new presentation of the natural concept of incompatibility, which generalizes inconsistency.