The lattice of all 4-valued implicative expansions of Belnap–Dunn logic containing Routley and Meyer’s basic logic Bd

[EN] The well-known logic first degree entailment logic (FDE), introduced by Belnap and Dunn, is defined with ∧, v and ~ as the sole primitive connectives. The aim of this paper is to establish the lattice formed by the class of all 4-valued C-extending implicative expansions of FDE verifying the ax...

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Detalhes bibliográficos
Autores: Robles Vázquez, Gemma, Méndez Rodríguez, José Manuel
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2024
País:España
Recursos:Universidad de León
Repositorio:BULERIA. Repositorio Institucional de la Universidad de León
OAI Identifier:oai:buleria.unileon.es:10612/22889
Acesso em linha:https://academic.oup.com/jigpal/article/32/3/493/7079130
https://hdl.handle.net/10612/22889
Access Level:acceso abierto
Palavra-chave:Lógica
Belnap–Dunn logic
Implicative expansions of Belnap–Dunn logic
Routley–Meyer basic logic B
Two-valued Belnap–Dunn semantics
Functional inclusion and equivalence
7205.02 Filosofía de la Lógica
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spelling The lattice of all 4-valued implicative expansions of Belnap–Dunn logic containing Routley and Meyer’s basic logic BdRobles Vázquez, GemmaMéndez Rodríguez, José ManuelLógicaBelnap–Dunn logicImplicative expansions of Belnap–Dunn logicRoutley–Meyer basic logic BTwo-valued Belnap–Dunn semanticsFunctional inclusion and equivalence7205.02 Filosofía de la Lógica[EN] The well-known logic first degree entailment logic (FDE), introduced by Belnap and Dunn, is defined with ∧, v and ~ as the sole primitive connectives. The aim of this paper is to establish the lattice formed by the class of all 4-valued C-extending implicative expansions of FDE verifying the axioms and rules of Routley and Meyer’s basic logic B and its useful disjunctive extension B^{d}. It is to be noted that Boolean negation (so, classical propositional logic) is definable in the strongest element in the said class.SIMinisterio de Ciencia e Innovación (10.13039/501100011033)Oxford AcademicLogica y Filosofia de la CienciaFacultad de Filosofia y Letras2024info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttps://academic.oup.com/jigpal/article/32/3/493/7079130https://hdl.handle.net/10612/22889reponame:BULERIA. Repositorio Institucional de la Universidad de Leóninstname:Universidad de LeónInglésinfo:eu-repo/grantAgreement/MCIN/AEI/Programa Estatal de Generación de Conocimiento y Fortalecimiento Científico y Tecnológico del Sistema de I+D+ihttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:buleria.unileon.es:10612/228892026-06-24T12:43:27Z
dc.title.none.fl_str_mv The lattice of all 4-valued implicative expansions of Belnap–Dunn logic containing Routley and Meyer’s basic logic Bd
title The lattice of all 4-valued implicative expansions of Belnap–Dunn logic containing Routley and Meyer’s basic logic Bd
spellingShingle The lattice of all 4-valued implicative expansions of Belnap–Dunn logic containing Routley and Meyer’s basic logic Bd
Robles Vázquez, Gemma
Lógica
Belnap–Dunn logic
Implicative expansions of Belnap–Dunn logic
Routley–Meyer basic logic B
Two-valued Belnap–Dunn semantics
Functional inclusion and equivalence
7205.02 Filosofía de la Lógica
title_short The lattice of all 4-valued implicative expansions of Belnap–Dunn logic containing Routley and Meyer’s basic logic Bd
title_full The lattice of all 4-valued implicative expansions of Belnap–Dunn logic containing Routley and Meyer’s basic logic Bd
title_fullStr The lattice of all 4-valued implicative expansions of Belnap–Dunn logic containing Routley and Meyer’s basic logic Bd
title_full_unstemmed The lattice of all 4-valued implicative expansions of Belnap–Dunn logic containing Routley and Meyer’s basic logic Bd
title_sort The lattice of all 4-valued implicative expansions of Belnap–Dunn logic containing Routley and Meyer’s basic logic Bd
dc.creator.none.fl_str_mv Robles Vázquez, Gemma
Méndez Rodríguez, José Manuel
author Robles Vázquez, Gemma
author_facet Robles Vázquez, Gemma
Méndez Rodríguez, José Manuel
author_role author
author2 Méndez Rodríguez, José Manuel
author2_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
Belnap–Dunn logic
Implicative expansions of Belnap–Dunn logic
Routley–Meyer basic logic B
Two-valued Belnap–Dunn semantics
Functional inclusion and equivalence
7205.02 Filosofía de la Lógica
topic Lógica
Belnap–Dunn logic
Implicative expansions of Belnap–Dunn logic
Routley–Meyer basic logic B
Two-valued Belnap–Dunn semantics
Functional inclusion and equivalence
7205.02 Filosofía de la Lógica
description [EN] The well-known logic first degree entailment logic (FDE), introduced by Belnap and Dunn, is defined with ∧, v and ~ as the sole primitive connectives. The aim of this paper is to establish the lattice formed by the class of all 4-valued C-extending implicative expansions of FDE verifying the axioms and rules of Routley and Meyer’s basic logic B and its useful disjunctive extension B^{d}. It is to be noted that Boolean negation (so, classical propositional logic) is definable in the strongest element in the said class.
publishDate 2024
dc.date.none.fl_str_mv 2024
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://academic.oup.com/jigpal/article/32/3/493/7079130
https://hdl.handle.net/10612/22889
url https://academic.oup.com/jigpal/article/32/3/493/7079130
https://hdl.handle.net/10612/22889
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/MCIN/AEI/Programa Estatal de Generación de Conocimiento y Fortalecimiento Científico y Tecnológico del Sistema de I+D+i
dc.rights.none.fl_str_mv http://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Oxford Academic
publisher.none.fl_str_mv Oxford Academic
dc.source.none.fl_str_mv reponame:BULERIA. Repositorio Institucional de la Universidad de León
instname:Universidad de León
instname_str Universidad de León
reponame_str BULERIA. Repositorio Institucional de la Universidad de León
collection BULERIA. Repositorio Institucional de la Universidad de León
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,81155

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