Logics of formal inconsistency arising from systems of fuzzy logic

TL;DR

This paper integrates paraconsistency into fuzzy logic by introducing operators for consistency and inconsistency, leading to new logical systems that are both fuzzy and paraconsistent, with formal axiomatizations over MTL-algebras.

Contribution

It defines postulates for consistency and inconsistency operators within MTL-based fuzzy logics, creating a novel family of paraconsistent fuzzy logics called LFIs.

Findings

Defined postulates for consistency and inconsistency operators over MTL-algebras

Axiomatized a family of fuzzy logics with paraconsistent properties

Established degree-preserving counterparts that are LFIs

Abstract

This paper proposes the meeting of fuzzy logic with paraconsistency in a very precise and foundational way. Specifically, in this paper we introduce expansions of the fuzzy logic MTL by means of primitive operators for consistency and inconsistency in the style of the so-called Logics of Formal Inconsistency (LFIs). The main novelty of the present approach is the definition of postulates for this type of operators over MTL-algebras, leading to the definition and axiomatization of a family of logics, expansions of MTL, whose degree-preserving counterpart are paraconsistent and moreover LFIs.