Paraconsistency and consistency understood as the absence of the negation of any implicative theorem
[EN] As is stated in its title, in this paper consistency is understood as the absence of the negation of any implicative theorem. Then, a series of logics adequate to this concept of consistency is defined within the context of the ternary relational semantics with a set of designated points, negat...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2012 |
| País: | España |
| Institución: | Universidad de León |
| Repositorio: | BULERIA. Repositorio Institucional de la Universidad de León |
| OAI Identifier: | oai:buleria.unileon.es:10612/25814 |
| Acceso en línea: | https://ejournals.eu/en/journal/reports-on-mathematical-logic/article/paraconsistency-and-consistency-understood-as-the-absence-of-the-negation-of-any-implicative-theorem https://hdl.handle.net/10612/25814 |
| Access Level: | acceso abierto |
| Palabra clave: | Lógica Paraconsistent logics Consistency 11 Lógica |
| Sumario: | [EN] As is stated in its title, in this paper consistency is understood as the absence of the negation of any implicative theorem. Then, a series of logics adequate to this concept of consistency is defined within the context of the ternary relational semantics with a set of designated points, negation being modelled with the Routley operator. Soundness and completeness theorems are provided for each one of these logics. In some cases, strong (i.e., in respect of deducibility) soundness and completeness theorems are also proven. All logics in this paper are included in Lewis’ S4. They are all paraconsistent, but none of them is relevant. |
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