Fidel Semantics for Propositional and First-Order Version of the Logic of CG(3)'

Autor(es)

Figallo-Orellano, A. ; Perez-Gaspar, M. ; Barcenas, E.

• Tipo de documento: Artigo Científico
• Fonte: LOGIC AND LOGICAL PHILOSOPHY; v. N/A, p. 18-pg., 2022-05-24.

Resumo

Paraconsistent extensions of 3-valued Godel 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(3)' is one of these 3-valued logics. In this paper, we introduce Fidel semantics for a certain calculus of CG(3)' by 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(3)' are presented by means of adapting algebraic tools. (AU)

• Processo FAPESP: 16/21928-0 - Semânticas não-determinísticas para as lógicas da inconsistência formal
• Beneficiário: Aldo Figallo Orellano
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado