Computational Aspects of Quasi-Classical Entailment

Abstract

Quasi-classical logic is a propositional logic for reasoning under inconsistency pointed out recently in the literature [3] [21]. Compared with several other paraconsistent logics, it has the nice feature that no special attention needs to be paid to a special form of premises (the connectives behave in a classical manner). However, only few is known about its computational behaviour up to now. In this paper, we fill this gap by pointing out a linear time translation that maps every instance of the quasi-classical entailment problem for CNF formulas into an instance of the classical entailment problem. This enables us to (1) show that quasi-classical entailment for CNF formulas is “only” coNP -complete, (2) take advantage of all existing automated reasoning techniques for classical entailment in order to improve quasi-classical inference from the practical side. Especially, tractable classes of formulas for quasi-classical entailment are pointed out.