Strengthening Brady’s Paraconsistent 4-Valued Logic BN4 with Truth-Functional Modal Operators

[EN] Łukasiewicz presented two different analyses of modal notions by means of many-valued logics: (1) the linearly ordered systems Ł3,...,Ł_{n} ,..., Ł_{w} ; (2) the 4-valued logic Ł he defined in the last years of his career. Unfortunately, all these systems contain “Łukasiewicz type (modal) parad...

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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:2016
País:España
Institución:Universidad de León
Repositorio:BULERIA. Repositorio Institucional de la Universidad de León
OAI Identifier:oai:buleria.unileon.es:10612/25704
Acceso en línea:https://link.springer.com/article/10.1007/s10849-016-9237-8
https://hdl.handle.net/10612/25704
Access Level:acceso abierto
Palabra clave:Lógica
Many-valued logics
Modal many-valued logics
Łukasiewicz many-valued logics
Łukasiewicz 4-valued modal logic
Brady’s 4-valued logic
Bilattice logics
Belnap-Dunn type bivalent semantics
11 Lógica
Descripción
Sumario:[EN] Łukasiewicz presented two different analyses of modal notions by means of many-valued logics: (1) the linearly ordered systems Ł3,...,Ł_{n} ,..., Ł_{w} ; (2) the 4-valued logic Ł he defined in the last years of his career. Unfortunately, all these systems contain “Łukasiewicz type (modal) paradoxes”. On the other hand, Brady’s 4-valued logic BN4 is the basic 4-valued bilattice logic. The aim of this paper is to show that BN4 can be strengthened with modal operators following Łukasiewicz’s strategy for defining truth-functional modal logics. The systems we define lack “Łukasiewicz type paradoxes”. Following Brady, we endow them with Belnap–Dunn type bivalent semantics.