Two 4-valued implicative expansions of first-degree entailment logic: the relevant logic BN4vsp and the (relevant) entailment logic BN4ap
[EN] A logic L has the "variable-sharing property" (VSP) if in all L-theorems of the form A -> B, A and B share at least a propositional variable. A logic L has the "Ackermann property" (AP) if in all L-theorems of the form A -> (B -> C), A contains at least a conditiona...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad de León |
| Repositorio: | BULERIA. Repositorio Institucional de la Universidad de León |
| OAI Identifier: | oai:buleria.unileon.es:10612/22890 |
| Acceso en línea: | https://academic.oup.com/logcom/article/33/2/462/7008709 https://hdl.handle.net/10612/22890 |
| Access Level: | acceso abierto |
| Palabra clave: | Lógica Relevant logics 4-valued relevant logics First-degree entailment logic Variable-sharing property Ackermann property Two-valued Belnap–Dunn semantics 11 Lógica |
| Sumario: | [EN] A logic L has the "variable-sharing property" (VSP) if in all L-theorems of the form A -> B, A and B share at least a propositional variable. A logic L has the "Ackermann property" (AP) if in all L-theorems of the form A -> (B -> C), A contains at least a conditional connective (->). Anderson and Belnap consider the VSP a necessary property of any relevant logic, and both the VSP and the AP necessary properties of any (relevant) entailment logic. Now, among relevant logicians, Brady’s logic BN4 is widely viewed as the adequate 4-valued implicative logic. But BN4 lacks the VSP and the AP. The aim of this paper is to define the logics BN4^{VSP} and BN4^{AP}. The former one has the VSP, whereas the latter one has the VSP and the AP. Moreover, both logics have some properties that do not support their consideration as mere artificial constructs. |
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