Abstract

A paraconsistent logic is one in which a nontrivial theory may include both a proposition and its negation. I will first introduce the general notion of a paraconsistent logic, and then analyze in detail the 3-valued paraconsistent logic J 3 . I will axiomatize J 3 , and in doing so will suggest that paraconsistent logics are inconsistent only with respect to classical semantics, not with respect to their own formal or informal semantic notions. An analysis of set-assignment semantics for J 3 will highlight the way in which the general framework for semantics of Chapter IV uses falsity as a default truth-value.

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