The quasi-relevant 3-valued logic RM3 and some of its sublogics lacking the variable-sharing property
[EN] The logic RM3 is the 3-valued extension of the logic R-Mingle (RM). RM (and so, RM3) does not have the variable- sharing property (vsp), but RM3 (and so, RM) lacks the more "offending" paradoxes of relevance", such as A → (B → A) or A → (A → B). Thus, RM and RM3 can be useful whe...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| 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:10612/25705 |
| Acceso en línea: | https://ejournals.eu/en/journal/reports-on-mathematical-logic/article/the-quasi-relevant-3-valued-logic-rm3-and-some-of-its-sublogics-lacking-the-variable-sharing-property https://hdl.handle.net/10612/25705 |
| Access Level: | acceso abierto |
| Palabra clave: | Lógica RM3 R-Mingle Relevant logics Quasi-relevant logics Routley- Meyer semantics Relational semantics Substructural logics 11 Lógica |
| Sumario: | [EN] The logic RM3 is the 3-valued extension of the logic R-Mingle (RM). RM (and so, RM3) does not have the variable- sharing property (vsp), but RM3 (and so, RM) lacks the more "offending" paradoxes of relevance", such as A → (B → A) or A → (A → B). Thus, RM and RM3 can be useful when some relevance", but not the full vsp, is needed. Sublogics of RM3 with the vsp are well known, but this is not the case with those lacking this property. The rst aim of this paper is to dene an ample family of sublogics of RM3 without the vsp. The second one is to provide these sublogics and RM3 itself with a general Routley-Meyer semantics, that is, the semantics devised for relevant logics in the early seventies of the past century. |
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