Implicative twist-structures

The twist-structure construction is used to represent algebras related to non-classical logics (e.g., Nelson algebras, bilattices) as a special kind of power of better-known algebraic structures (distributive lattices, Heyting algebras). We study a specific type of twist-structure (called implicativ...

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Detalles Bibliográficos
Autor: Rivieccio, Umberto
Tipo de recurso: artículo
Fecha de publicación:2014
País:España
Institución:Universidad Nacional de Educación a Distancia
Repositorio:e-spacio. Repositorio Institucional de la UNED
Idioma:inglés
OAI Identifier:oai:e-spacio.uned.es:20.500.14468/24643
Acceso en línea:https://hdl.handle.net/20.500.14468/24643
Access Level:acceso abierto
Palabra clave:11 Lógica
twist-structure
implicative bilattice
N4-lattice
Nelson lattice
representation
subreducts
algebraic logic
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spelling Implicative twist-structuresRivieccio, Umberto11 Lógicatwist-structureimplicative bilatticeN4-latticeNelson latticerepresentationsubreductsalgebraic logicThe twist-structure construction is used to represent algebras related to non-classical logics (e.g., Nelson algebras, bilattices) as a special kind of power of better-known algebraic structures (distributive lattices, Heyting algebras). We study a specific type of twist-structure (called implicative twist-structure) obtained as a power of a generalized Boolean algebra, focusing on the implication-negation fragment of the usual algebraic language of twist-structures. We prove that implicative twist-structures form a variety which is semisimple, congruence-distributive, finitely generated, and has equationally definable principal congruences. We characterize the congruences of each algebra in the variety in terms of the congruences of the associated generalized Boolean algebra. We classify and axiomatize the subvarieties of implicative twist-structures. We define a corresponding logic and prove that it is algebraizable with respect to our variety.Springer Alemaniae-Spacio UNED20242024-12-0220142014-09-0320142014-09-03journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14468/24643reponame:e-spacio. Repositorio Institucional de la UNEDinstname:Universidad Nacional de Educación a DistanciaInglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-nd/4.0/deed.esoai:e-spacio.uned.es:20.500.14468/246432026-06-06T12:38:31Z
dc.title.none.fl_str_mv Implicative twist-structures
title Implicative twist-structures
spellingShingle Implicative twist-structures
Rivieccio, Umberto
11 Lógica
twist-structure
implicative bilattice
N4-lattice
Nelson lattice
representation
subreducts
algebraic logic
title_short Implicative twist-structures
title_full Implicative twist-structures
title_fullStr Implicative twist-structures
title_full_unstemmed Implicative twist-structures
title_sort Implicative twist-structures
dc.creator.none.fl_str_mv Rivieccio, Umberto
author Rivieccio, Umberto
author_facet Rivieccio, Umberto
author_role author
dc.contributor.none.fl_str_mv e-Spacio UNED
dc.subject.none.fl_str_mv 11 Lógica
twist-structure
implicative bilattice
N4-lattice
Nelson lattice
representation
subreducts
algebraic logic
topic 11 Lógica
twist-structure
implicative bilattice
N4-lattice
Nelson lattice
representation
subreducts
algebraic logic
description The twist-structure construction is used to represent algebras related to non-classical logics (e.g., Nelson algebras, bilattices) as a special kind of power of better-known algebraic structures (distributive lattices, Heyting algebras). We study a specific type of twist-structure (called implicative twist-structure) obtained as a power of a generalized Boolean algebra, focusing on the implication-negation fragment of the usual algebraic language of twist-structures. We prove that implicative twist-structures form a variety which is semisimple, congruence-distributive, finitely generated, and has equationally definable principal congruences. We characterize the congruences of each algebra in the variety in terms of the congruences of the associated generalized Boolean algebra. We classify and axiomatize the subvarieties of implicative twist-structures. We define a corresponding logic and prove that it is algebraizable with respect to our variety.
publishDate 2014
dc.date.none.fl_str_mv 2014
2014-09-03
2014
2014-09-03
2024
2024-12-02
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14468/24643
url https://hdl.handle.net/20.500.14468/24643
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
http://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer Alemania
publisher.none.fl_str_mv Springer Alemania
dc.source.none.fl_str_mv reponame:e-spacio. Repositorio Institucional de la UNED
instname:Universidad Nacional de Educación a Distancia
instname_str Universidad Nacional de Educación a Distancia
reponame_str e-spacio. Repositorio Institucional de la UNED
collection e-spacio. Repositorio Institucional de la UNED
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,811543

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