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