A classical-logic view of a paraconsistent logic

Abstract: This paper is concerned with the first-order paraconsistent logic LPQ$^{\supset,\mathsf{F}}$. 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$^{\supset,\mathsf{F}}$ and a logical justification of its proof system. The major properties of this logic are also treated.