Abstract

PEREZ-GASPAR, Miguel  and  BARCENAS, Everardo. On the Algebrization of the Multi-valued Logics CG′₃ and G′₃. Comp. y Sist. [online]. 2021, vol.25, n.4, pp.751-759.  Epub Feb 28, 2022. ISSN 2007-9737.  https://doi.org/10.13053/cys-25-4-4046.

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 even in the construction of paraconsistent neural networks. ${G^{\prime }}_3$ is a 3-valued logic with a single represented truth value by 1. $C{G^{\prime }}_3$ is a paraconsistent, 3-valued logic that extends ${G^{\prime }}_3$ with two truth values represented by 1 and 2. The state of the art of $C{G^{\prime }}_3$ comprises a Kripke semantics and a Hilbert axiomatization inspired by the Lindenbaum-Łos technique. In this work, we show that ${G^{\prime }}_3$ and $C{G^{\prime }}_3$ are algebrizable in the sense of Blok and Pigozzi. These results may apply to the development of paraconsistent reasoning systems.

Keywords : Paraconsistent logics; blok-pigozzi algebrization; non-monotonic reasoning.

        · text in English     · English ( pdf )