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- Title
Fidel Semantics for Propositional and First-Order Version of the Logic of CG'<sub>3</sub>.
- Authors
Figallo-Orellano, A.; Pérez-Gaspar, M.; Bárcenas, E.
- 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'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.
- Subjects
NONMONOTONIC logic; FIRST-order logic; SEMANTICS; KNOWLEDGE representation (Information theory); BOOLEAN algebra
- Publication
Logic & Logical Philosophy, 2023, Vol 32, Issue 1, p141
- ISSN
1425-3305
- Publication type
Article
- DOI
10.12775/LLP.2022.019