On the Algebrization of the Multi-valued Logics CG´3 and G´3

Abstract

Multi-valued logics form a family of formal languages with several applications in computer sciences, particularly in the field of Artificial intelligence. Paraconsistent multi-valued logics have been successful applied in logic programming, fuzzy reasoning, and evenin the construction of paraconsistent neural networks. G03 is a 3-valued logic with a single represented truth value by 1. CG´3 is a paraconsistent, 3-valued logic that extends G´3 with two truth values represented by 1 and 2. The state of the art of CG´3 comprises a Kripkesemantics and a Hilbert axiomatization inspired by the Lindenbaum-Łos technique. In this work, we show that G´3 and CG´3 are algebrizable in the sense of Blok and Pigozzi. These results may apply to the development of paraconsistent reasoning systems.