Negation-Free Definitions of Paraconsistency

TL;DR

This paper explores whether paraconsistency can be defined without negation, introducing two negation-free notions and a connective called 'fusion' to characterize paraconsistency.

Contribution

It presents the first negation-free definitions of paraconsistency, including a connective-based approach and a derived quasi-negation, expanding the conceptual framework.

Findings

Negation-free paraconsistency notions are feasible.

A 'fusion' connective can be used to define paraconsistency without negation.

Derived quasi-negation has specific logical properties.

Abstract

Paraconsistency is commonly defined and/or characterized as the failure of a principle of explosion. The various standard forms of explosion involve one or more logical operators or connectives, among which the negation operator is the most frequent. In this article, we ask whether a negation operator is essential for describing paraconsistency. In other words, is it possible to describe a notion of paraconsistency that is independent of connectives? We present two such notions of negation-free paraconsistency, one that is completely independent of connectives and another that uses a conjunction-like binary connective that we call 'fusion'. We also derive a notion of 'quasi-negation' from the former, and investigate its properties.