A classical-logic view of a paraconsistent logic

08/17/2020

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by   C. A. Middelburg, et al.

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This paper is concerned with the first-order paraconsistent logic LPQ^⊃,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^⊃,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.