A classical-logic view of a paraconsistent logic.

Abstract

This paper is concerned with the first-order paraconsistent logic LPQ $^{\supset,F}$. A sequent-style natural deduction proof system for this logic is presented and, for this proof system, both a model-theoretic justification and a logical justification by means of an embedding into first-order classical logic is given. The given embedding provides both a classical-logic explanation of LPQ$^{\supset,F}$ and a logical justification of its proof system. The major properties of this logic are also treated.