Monotonic Distributive Semilattices

Autores
Celani, Sergio Arturo; Menchón, María Paula
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In the study of algebras related to non-classical logics, (distributive) semilattices are always present in the background. For example, the algebraic semantic of the {→, ∧, ⊤}-fragment of intuitionistic logic is the variety of implicative meet-semilattices (Chellas 1980; Hansen 2003). In this paper we introduce and study the class of distributive meet-semilattices endowed with a monotonic modal operator m. We study the representation theory of these algebras using the theory of canonical extensions and we give a topological duality for them. Also, we show how our new duality extends to some particular subclasses.
Fil: Celani, Sergio Arturo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Departamento de Matemática; Argentina
Fil: Menchón, María Paula. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
DISTRIBUTIVE MEET SEMILATTICES
DS-SPACES
MODAL OPERATORS
MONOTONIC MODAL LOGICS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/96559
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Monotonic Distributive SemilatticesCelani, Sergio ArturoMenchón, María PaulaDISTRIBUTIVE MEET SEMILATTICESDS-SPACESMODAL OPERATORSMONOTONIC MODAL LOGICShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In the study of algebras related to non-classical logics, (distributive) semilattices are always present in the background. For example, the algebraic semantic of the {→, ∧, ⊤}-fragment of intuitionistic logic is the variety of implicative meet-semilattices (Chellas 1980; Hansen 2003). In this paper we introduce and study the class of distributive meet-semilattices endowed with a monotonic modal operator m. We study the representation theory of these algebras using the theory of canonical extensions and we give a topological duality for them. Also, we show how our new duality extends to some particular subclasses.Fil: Celani, Sergio Arturo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Departamento de Matemática; ArgentinaFil: Menchón, María Paula. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaSpringer2019-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/96559Celani, Sergio Arturo; Menchón, María Paula; Monotonic Distributive Semilattices; Springer; Order; 36; 3; 11-2019; 463-4860167-8094CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s11083-018-9477-0info:eu-repo/semantics/altIdentifier/doi/10.1007/s11083-018-9477-0info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1810.08585info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:27:56Zoai:ri.conicet.gov.ar:11336/96559instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:27:57.094CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Monotonic Distributive Semilattices
title Monotonic Distributive Semilattices
spellingShingle Monotonic Distributive Semilattices
Celani, Sergio Arturo
DISTRIBUTIVE MEET SEMILATTICES
DS-SPACES
MODAL OPERATORS
MONOTONIC MODAL LOGICS
title_short Monotonic Distributive Semilattices
title_full Monotonic Distributive Semilattices
title_fullStr Monotonic Distributive Semilattices
title_full_unstemmed Monotonic Distributive Semilattices
title_sort Monotonic Distributive Semilattices
dc.creator.none.fl_str_mv Celani, Sergio Arturo
Menchón, María Paula
author Celani, Sergio Arturo
author_facet Celani, Sergio Arturo
Menchón, María Paula
author_role author
author2 Menchón, María Paula
author2_role author
dc.subject.none.fl_str_mv DISTRIBUTIVE MEET SEMILATTICES
DS-SPACES
MODAL OPERATORS
MONOTONIC MODAL LOGICS
topic DISTRIBUTIVE MEET SEMILATTICES
DS-SPACES
MODAL OPERATORS
MONOTONIC MODAL LOGICS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In the study of algebras related to non-classical logics, (distributive) semilattices are always present in the background. For example, the algebraic semantic of the {→, ∧, ⊤}-fragment of intuitionistic logic is the variety of implicative meet-semilattices (Chellas 1980; Hansen 2003). In this paper we introduce and study the class of distributive meet-semilattices endowed with a monotonic modal operator m. We study the representation theory of these algebras using the theory of canonical extensions and we give a topological duality for them. Also, we show how our new duality extends to some particular subclasses.
Fil: Celani, Sergio Arturo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Departamento de Matemática; Argentina
Fil: Menchón, María Paula. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description In the study of algebras related to non-classical logics, (distributive) semilattices are always present in the background. For example, the algebraic semantic of the {→, ∧, ⊤}-fragment of intuitionistic logic is the variety of implicative meet-semilattices (Chellas 1980; Hansen 2003). In this paper we introduce and study the class of distributive meet-semilattices endowed with a monotonic modal operator m. We study the representation theory of these algebras using the theory of canonical extensions and we give a topological duality for them. Also, we show how our new duality extends to some particular subclasses.
publishDate 2019
dc.date.none.fl_str_mv 2019-11
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/96559
Celani, Sergio Arturo; Menchón, María Paula; Monotonic Distributive Semilattices; Springer; Order; 36; 3; 11-2019; 463-486
0167-8094
CONICET Digital
CONICET
url http://hdl.handle.net/11336/96559
identifier_str_mv Celani, Sergio Arturo; Menchón, María Paula; Monotonic Distributive Semilattices; Springer; Order; 36; 3; 11-2019; 463-486
0167-8094
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s11083-018-9477-0
info:eu-repo/semantics/altIdentifier/doi/10.1007/s11083-018-9477-0
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1810.08585
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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