On The Paraconsistent Logic Cg '(3)

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 a 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 Kalmar's approach; and a new notion of validity, based on also novel Kripke semantics.