A Strong and Rich 4-Valued Modal Logic Without Łukasiewicz-Type Paradoxes

[EN] The aim of this paper is to introduce an alternative to Łukasiewicz’s 4-valued modal logic Ł. As it is known, Ł is afflicted by “Łukasiewicz (modal) type paradoxes”. The logic we define, PŁ4, is a strong paraconsistent and paracomplete 4-valued modal logic free from this type of paradoxes. PŁ4...

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Detalles Bibliográficos
Autores: Méndez Rodríguez, José Manuel, Robles Vázquez, Gemma
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2015
País:España
Institución:Universidad de León
Repositorio:BULERIA. Repositorio Institucional de la Universidad de León
OAI Identifier:oai:buleria.unileon.es:10612/25727
Acceso en línea:https://link.springer.com/article/10.1007/s11787-015-0130-z
https://hdl.handle.net/10612/25727
Access Level:acceso abierto
Palabra clave:Lógica
Many-valued logics
Modal logics
Paraconsistent logics
Paracomplete logics
4-valued modal logics
Łukasiewicz 4-valued modal logic
Belnap-Dunn type semantics
11 Lógica
Descripción
Sumario:[EN] The aim of this paper is to introduce an alternative to Łukasiewicz’s 4-valued modal logic Ł. As it is known, Ł is afflicted by “Łukasiewicz (modal) type paradoxes”. The logic we define, PŁ4, is a strong paraconsistent and paracomplete 4-valued modal logic free from this type of paradoxes. PŁ4 is determined by the degree of truth-preserving consequence relation defined on the ordered set of values of a modification of the matrix MŁ characteristic for the logic Ł. On the other hand, PŁ4 is a rich logic in which a number of connectives can be defined. It also has a simple bivalent semantics of the Belnap–Dunn type.