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
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