Generalized explosion principles

TL;DR

This paper explores generalized explosion principles in logic, proposing negation-free formulations of paraconsistency and examining how explosion can occur without negation, especially in logics of formal inconsistency.

Contribution

It introduces negation-free principles of explosion and paraconsistency, expanding understanding beyond traditional negation-based frameworks.

Findings

Negation-free paraconsistency is possible with generalized explosion principles.

A notion of quasi-negation is derived and analyzed.

Explosion can occur in the presence of additional information, not just negation.

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 and primary. In this article, we start by asking whether a negation operator is essential for describing explosion and paraconsistency. In other words, is it possible to describe a principle of explosion and hence a notion of paraconsistency that is independent of connectives? A negation-free paraconsistency resulting from the failure of a generalized principle of explosion is presented first. We also derive a notion of quasi-negation from this and investigate its properties. Next, more general principles of explosion are considered. These are also negation-free; moreover, these principles gradually move away from the idea that an explosion requires a statement and its opposite. Thus, these principles can capture the explosion observed in logics where a statement and its negation explode only in the presence of additional information, such as in the logics of formal inconsistency.