Fidel Semantics for Propositional and First-Order Version of the Logic of CG’3

Aldo Figallo Orellano; Miguel Pérez-Gaspar; Everardo Bárcenas

doi:10.12775/LLP.2022.019

Authors

Aldo Figallo Orellano https://orcid.org/0000-0001-5844-3371
Miguel Pérez-Gaspar Facultad de Ingeniería Universidad Nacional Autónoma de México (UNAM)
Everardo Bárcenas Facultad de Ingeniería Universidad Nacional Autónoma de México (UNAM) https://orcid.org/0000-0002-1523-1579

DOI:

https://doi.org/10.12775/LLP.2022.019

Keywords

paraconsistent logics, first-order logics, Fidel semantics

Abstract

Paraconsistent extensions of 3-valued Gödel logic are studied as tools for knowledge representation and nonmonotonic reasoning. Particularly, Osorio and his collaborators showed that some of these logics can be used to express interesting nonmonotonic semantics. CG’₃is one of these 3-valued logics. In this paper, we introduce Fidel semantics for a certain calculus of CG’₃by means of Fidel structures, named CG’₃-structures. These structures are constructed from enriched Boolean algebras with a special family of sets. Moreover, we also show that the most basic CG’₃-structures coincide with da Costa–Alves’ bi-valuation semantics; this connection is displayed through a Representation Theorem for CG’₃-structures. By contrast, we show that for other paraconsistent logics that allow us to present semantics through Fidel structures, this connection is not held. Finally, Fidel semantics for the first-order version of the logic of CG’₃are presented by means of adapting algebraic tools.

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