CONSEQUENCE AND INCONSISTENCY: PARACONSISTENT LOGICS

Classically the notions of consequence and inconsistency are interwoven. That is, considering one as the primitive notion the other can be derived. This equivalence depends on the notions of absolute inconsistency and negation inconsistency, which are equivalent in classical scenario. Absolute inconsistency states that given any formula a and its negation -a, {a, -a} yields any formula b. On the other hand, according to the notion of negation inconsistency, a set is said to be inconsistent if for some formula a, both a, -a follows from the set. In the context of paraconsistent logics this equivalence between absolute inconsistency and negation inconsistency does not work. So, the interrelation between consequence and inconsistency in the context of paraconsistent logics seems to be an interesting direction to be explored. In this presentation we shall concentrate on different fragments of a propositional language, and explore the connection between the notion of consequence and inconsistency where the consequence is nonexplosive.

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