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...
| Autores: | , |
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| 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 |
| 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. |
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