Logics of formal inconsistency arising from systems of fuzzy logic
This work addresses foundational issues in logic for researchers in fuzzy and paraconsistent logic, but it appears incremental as it builds on existing MTL frameworks.
The paper tackles the integration of fuzzy logic with paraconsistency by introducing expansions of the fuzzy logic MTL with operators for consistency and inconsistency, resulting in a family of logics that are paraconsistent and classified as Logics of Formal Inconsistency.
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.