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 given 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 presented. For no logic that is essentially the same as LPQ$^{\supset,F}$, a natural deduction proof system is currently available in the literature. The presented embedding provides both a classical-logic explanation of this logic and a logical justification of its proof system.