On the Paraconsistent Logic CG′3

Abstract

Paraconsistent logical systems are well-known reasoning frameworks aimed to infer new facts or properties under contradictory assumptions. Applications of these systems are well known in wide range of computer science domains. In this article, we study the paraconsistent logic CG ′ 3 , which can be viewed as an extension of the logic G ′ 3 . CG ′ 3 is also 3 -valued, but with two designated values. Main results can be summarized as follows: a Hilbert-type axiomatization, based on Kalmár’s approach; and a new notion of validity, based on also novel Kripke semantics.