12/11 - Francesc Esteva* & Lluis Godo*
On paraconsistent fuzzy logics
Paraconsistent logics are specially tailored to deal with inconsistency, while fuzzy logics primarily deal with graded truth and vagueness. Aiming at studying logics that can handle inconsistency and graded truth at once, this talk will report about recent investigations on how a notion of paraconsistent fuzzy logic can be cast within the framework of the so-called logics of formal inconsistency (LFIs).
As in classical logic, it is clear that the notion of truth-preserving deduction commonly used in systems of mathematical fuzzy logic is incompatible with any form of paraconsistency. However, in the first part of the seminar we will show that, instead, some degree-preserving fuzzy logics exhibit interesting paraconsistency features. We will also consider expansions of these logics with additional negation connectives and study their paraconsistency properties as LFIs.
In the second part of the seminar, we will address a kind of converse problem, namely how to extend a given fuzzy logic with a new “consistency” operator in the style of the LFIs. We will introduce a set of postulates for this type of operators over the corresponding algebras, leading to the definition and axiomatization of a family of logics, expansions of MTL, whose degree-preserving counterpart are paraconsistent and moreover LFIs.
In the third and final part of the seminar, we will talk about some remarks on ongoing work on the study on intermediate paraconsistent fuzzy logics between the truth-preserving and degree-preserving logics.
*IIIA - CSIC, Barcelona, Spain