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...
| Autor: | |
|---|---|
| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2012 |
| País: | España |
| Recursos: | Universidad de León |
| Repositorio: | BULERIA. Repositorio Institucional de la Universidad de León |
| OAI Identifier: | oai:buleria.unileon.es:10612/25814 |
| Acesso em linha: | 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 |
| Palavra-chave: | Lógica Paraconsistent logics Consistency 11 Lógica |
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Paraconsistency and consistency understood as the absence of the negation of any implicative theoremRobles, GemmaLógicaParaconsistent logicsConsistency11 Lógica[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.SIMinisterio de Ciencia e Innovación (España)Jagiellonian UniversityLogica y Filosofia de la CienciaFacultad de Filosofia y Letras2012info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttps://ejournals.eu/en/journal/reports-on-mathematical-logic/article/paraconsistency-and-consistency-understood-as-the-absence-of-the-negation-of-any-implicative-theoremhttps://hdl.handle.net/10612/25814reponame:BULERIA. Repositorio Institucional de la Universidad de Leóninstname:Universidad de LeónInglésinfo:eu-repo/grantAgreement/MINECO//FFI2008-05859info:eu-repo/grantAgreement/MINECO//FFI2011-28494http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:buleria.unileon.es:10612/258142026-06-24T12:43:27Z |
| dc.title.none.fl_str_mv |
Paraconsistency and consistency understood as the absence of the negation of any implicative theorem |
| title |
Paraconsistency and consistency understood as the absence of the negation of any implicative theorem |
| spellingShingle |
Paraconsistency and consistency understood as the absence of the negation of any implicative theorem Robles, Gemma Lógica Paraconsistent logics Consistency 11 Lógica |
| title_short |
Paraconsistency and consistency understood as the absence of the negation of any implicative theorem |
| title_full |
Paraconsistency and consistency understood as the absence of the negation of any implicative theorem |
| title_fullStr |
Paraconsistency and consistency understood as the absence of the negation of any implicative theorem |
| title_full_unstemmed |
Paraconsistency and consistency understood as the absence of the negation of any implicative theorem |
| title_sort |
Paraconsistency and consistency understood as the absence of the negation of any implicative theorem |
| dc.creator.none.fl_str_mv |
Robles, Gemma |
| author |
Robles, Gemma |
| author_facet |
Robles, Gemma |
| author_role |
author |
| dc.contributor.none.fl_str_mv |
Logica y Filosofia de la Ciencia Facultad de Filosofia y Letras |
| dc.subject.none.fl_str_mv |
Lógica Paraconsistent logics Consistency 11 Lógica |
| topic |
Lógica Paraconsistent logics Consistency 11 Lógica |
| description |
[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. |
| publishDate |
2012 |
| dc.date.none.fl_str_mv |
2012 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
| format |
article |
| status_str |
publishedVersion |
| dc.identifier.none.fl_str_mv |
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 |
| url |
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 |
| dc.language.none.fl_str_mv |
Inglés |
| language_invalid_str_mv |
Inglés |
| dc.relation.none.fl_str_mv |
info:eu-repo/grantAgreement/MINECO//FFI2008-05859 info:eu-repo/grantAgreement/MINECO//FFI2011-28494 |
| dc.rights.none.fl_str_mv |
http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ |
| eu_rights_str_mv |
openAccess |
| dc.publisher.none.fl_str_mv |
Jagiellonian University |
| publisher.none.fl_str_mv |
Jagiellonian University |
| dc.source.none.fl_str_mv |
reponame:BULERIA. Repositorio Institucional de la Universidad de León instname:Universidad de León |
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Universidad de León |
| reponame_str |
BULERIA. Repositorio Institucional de la Universidad de León |
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BULERIA. Repositorio Institucional de la Universidad de León |
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1869403316888272896 |
| score |
15,81155 |