Modal operators for meet-complemented lattices

Autores
Castiglioni, José Luis; Ertola Biraben, Rodolfo Cristian
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Weinvestigate some modal operators of necessity and possibility that form an adjoint pair in the context of meet-complemented lattices. We prove that they form an equational class and we study the modalities, i.e. the finite sequences of unary operators. We proceed in stages, first considering the not necessarily distributive case and also considering the case with the algebraic version of the 4 axiom in modal logic. We compare our operators with other operators in the literature, to wit, the maximum Boolean below and operations defined using the dual of the meet-complement.
Fil: Castiglioni, José Luis. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Cidade Universitária; Brasil
Fil: Ertola Biraben, Rodolfo Cristian. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Cidade Universitária; Brasil
Materia
Meet-Complemented Lattices
Modal Operators
Necessity
Non-Distributive Lattices
Possibility
Univocally Defined Operations
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:11336/49715
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/49715
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Modal operators for meet-complemented latticesCastiglioni, José LuisErtola Biraben, Rodolfo CristianMeet-Complemented LatticesModal OperatorsNecessityNon-Distributive LatticesPossibilityUnivocally Defined Operationshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Weinvestigate some modal operators of necessity and possibility that form an adjoint pair in the context of meet-complemented lattices. We prove that they form an equational class and we study the modalities, i.e. the finite sequences of unary operators. We proceed in stages, first considering the not necessarily distributive case and also considering the case with the algebraic version of the 4 axiom in modal logic. We compare our operators with other operators in the literature, to wit, the maximum Boolean below and operations defined using the dual of the meet-complement.Fil: Castiglioni, José Luis. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Cidade Universitária; BrasilFil: Ertola Biraben, Rodolfo Cristian. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Cidade Universitária; BrasilOxford University Press2017-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/49715Castiglioni, José Luis; Ertola Biraben, Rodolfo Cristian; Modal operators for meet-complemented lattices; Oxford University Press; Logic Journal of the IGPL (print); 25; 4; 8-2017; 465-4951367-0751CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1093/jigpal/jzx011info:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/jigpal/article-abstract/25/4/465/3896873info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:34:38Zoai:ri.conicet.gov.ar:11336/49715instacron: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 09:34:38.443CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Modal operators for meet-complemented lattices
title Modal operators for meet-complemented lattices
spellingShingle Modal operators for meet-complemented lattices
Castiglioni, José Luis
Meet-Complemented Lattices
Modal Operators
Necessity
Non-Distributive Lattices
Possibility
Univocally Defined Operations
title_short Modal operators for meet-complemented lattices
title_full Modal operators for meet-complemented lattices
title_fullStr Modal operators for meet-complemented lattices
title_full_unstemmed Modal operators for meet-complemented lattices
title_sort Modal operators for meet-complemented lattices
dc.creator.none.fl_str_mv Castiglioni, José Luis
Ertola Biraben, Rodolfo Cristian
author Castiglioni, José Luis
author_facet Castiglioni, José Luis
Ertola Biraben, Rodolfo Cristian
author_role author
author2 Ertola Biraben, Rodolfo Cristian
author2_role author
dc.subject.none.fl_str_mv Meet-Complemented Lattices
Modal Operators
Necessity
Non-Distributive Lattices
Possibility
Univocally Defined Operations
topic Meet-Complemented Lattices
Modal Operators
Necessity
Non-Distributive Lattices
Possibility
Univocally Defined Operations
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Weinvestigate some modal operators of necessity and possibility that form an adjoint pair in the context of meet-complemented lattices. We prove that they form an equational class and we study the modalities, i.e. the finite sequences of unary operators. We proceed in stages, first considering the not necessarily distributive case and also considering the case with the algebraic version of the 4 axiom in modal logic. We compare our operators with other operators in the literature, to wit, the maximum Boolean below and operations defined using the dual of the meet-complement.
Fil: Castiglioni, José Luis. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Cidade Universitária; Brasil
Fil: Ertola Biraben, Rodolfo Cristian. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Cidade Universitária; Brasil
description Weinvestigate some modal operators of necessity and possibility that form an adjoint pair in the context of meet-complemented lattices. We prove that they form an equational class and we study the modalities, i.e. the finite sequences of unary operators. We proceed in stages, first considering the not necessarily distributive case and also considering the case with the algebraic version of the 4 axiom in modal logic. We compare our operators with other operators in the literature, to wit, the maximum Boolean below and operations defined using the dual of the meet-complement.
publishDate 2017
dc.date.none.fl_str_mv 2017-08
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/11336/49715
Castiglioni, José Luis; Ertola Biraben, Rodolfo Cristian; Modal operators for meet-complemented lattices; Oxford University Press; Logic Journal of the IGPL (print); 25; 4; 8-2017; 465-495
1367-0751
CONICET Digital
CONICET
url http://hdl.handle.net/11336/49715
identifier_str_mv Castiglioni, José Luis; Ertola Biraben, Rodolfo Cristian; Modal operators for meet-complemented lattices; Oxford University Press; Logic Journal of the IGPL (print); 25; 4; 8-2017; 465-495
1367-0751
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1093/jigpal/jzx011
info:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/jigpal/article-abstract/25/4/465/3896873
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
dc.publisher.none.fl_str_mv Oxford University Press
publisher.none.fl_str_mv Oxford University Press
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
_version_ 1844613073209393152
score 13.070432

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