A Class of Implicative Expansions of Belnap-Dunn Logic in which Boolean Negation is Definable

[EN] Belnap and Dunn’s well-known 4-valued logic FDE is an interesting and useful non-classical logic. FDE is defined by using conjunction, disjunction and negation as the sole propositional connectives. Then the question of expanding FDE with an implication connective is of course of great interest...

Descripción completa

Detalles Bibliográficos
Autores: Robles Vázquez, Gemma, Méndez Rodríguez, José Manuel
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2023
País:España
Institución:Universidad de León
Repositorio:BULERIA. Repositorio Institucional de la Universidad de León
OAI Identifier:oai:buleria.unileon.es:10612/22904
Acceso en línea:https://link.springer.com/article/10.1007/s10992-022-09692-2
https://hdl.handle.net/10612/22904
Access Level:acceso abierto
Palabra clave:Lógica
Belnap-Dunn logic
Implicative expansions of Belnap-Dunn logic
Boolean negation
Two-valued Belnap-Dunn semantics
11 Lógica
Descripción
Sumario:[EN] Belnap and Dunn’s well-known 4-valued logic FDE is an interesting and useful non-classical logic. FDE is defined by using conjunction, disjunction and negation as the sole propositional connectives. Then the question of expanding FDE with an implication connective is of course of great interest. In this sense, some implicative expansions of FDE have been proposed in the literature, among which Brady’s logic BN4 seems to be the preferred option of relevant logicians. The aim of this paper is to define a class of implicative expansions of FDE in whose elements Boolean negation is definable, whence strong logics such as the paraconsistent and paracomplete logic PŁ4 and BN4 itself are definable, in addition to classical propositional logic.