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...

Descripción completa

Detalles Bibliográficos
Autor: Robles, Gemma
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
Descripción
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.