Monadic Pseudocomplemented Distributive Lattices

Autores
Calomino, Ismael; Lewis Smith, Andrew; Pelaitay, Gustavo Andrés
Año de publicación
2025
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper, we study the variety of pseudocomplemented distributive lattices with existential and universal quantifiers, called monadic pseudocomplemented distributive lattices. We introduce the variety of monadic KANalgebras, which turns out to be different from the class studied in [Gomez C., Marcos M., San Martín H.J.: On the relation of negations in Nelson algebras. Rep. Math. Logic 56 (2021), 15–56], and prove that the category of monadic pseudocomplemented distributive lattices is equivalent to the category of centered monadic KAN-algebras, extending the results given in [Calomino I., Pelaitay G.: A new categorical equivalence for Stone algebras. Accepted in Mathematica Slovaca (2025)]
Fil: Calomino, Ismael. Universidad Católica de Ávila; España
Fil: Lewis Smith, Andrew. Middlesex University; Reino Unido
Fil: Pelaitay, Gustavo Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; Argentina. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Instituto de Ciencias Básicas; Argentina
Materia
Monadic Pseudocomplemented Distributive Lattices
KALMAN CONSTRUCTION
MONADIC KAN-ALGEBRAS
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:11336/281009
Acceder
id CONICETDig_61b6130e791ced324433bdee47f91f2e
oai_identifier_str oai:ri.conicet.gov.ar:11336/281009
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Monadic Pseudocomplemented Distributive LatticesCalomino, IsmaelLewis Smith, AndrewPelaitay, Gustavo AndrésMonadic Pseudocomplemented Distributive LatticesKALMAN CONSTRUCTIONMONADIC KAN-ALGEBRAShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper, we study the variety of pseudocomplemented distributive lattices with existential and universal quantifiers, called monadic pseudocomplemented distributive lattices. We introduce the variety of monadic KANalgebras, which turns out to be different from the class studied in [Gomez C., Marcos M., San Martín H.J.: On the relation of negations in Nelson algebras. Rep. Math. Logic 56 (2021), 15–56], and prove that the category of monadic pseudocomplemented distributive lattices is equivalent to the category of centered monadic KAN-algebras, extending the results given in [Calomino I., Pelaitay G.: A new categorical equivalence for Stone algebras. Accepted in Mathematica Slovaca (2025)]Fil: Calomino, Ismael. Universidad Católica de Ávila; EspañaFil: Lewis Smith, Andrew. Middlesex University; Reino UnidoFil: Pelaitay, Gustavo Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; Argentina. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Instituto de Ciencias Básicas; ArgentinaCollege Publications2025-12info: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/11336/281009Calomino, Ismael; Lewis Smith, Andrew; Pelaitay, Gustavo Andrés; Monadic Pseudocomplemented Distributive Lattices; College Publications; Journal of Applied Logics; 12; 7; 12-2025; 2009-20362631-98102631-9829CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.collegepublications.co.uk/ifcolog/?00075info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2026-02-26T10:24:53Zoai:ri.conicet.gov.ar:11336/281009instacron: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:34982026-02-26 10:24:53.53CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Monadic Pseudocomplemented Distributive Lattices
title Monadic Pseudocomplemented Distributive Lattices
spellingShingle Monadic Pseudocomplemented Distributive Lattices
Calomino, Ismael
Monadic Pseudocomplemented Distributive Lattices
KALMAN CONSTRUCTION
MONADIC KAN-ALGEBRAS
title_short Monadic Pseudocomplemented Distributive Lattices
title_full Monadic Pseudocomplemented Distributive Lattices
title_fullStr Monadic Pseudocomplemented Distributive Lattices
title_full_unstemmed Monadic Pseudocomplemented Distributive Lattices
title_sort Monadic Pseudocomplemented Distributive Lattices
dc.creator.none.fl_str_mv Calomino, Ismael
Lewis Smith, Andrew
Pelaitay, Gustavo Andrés
author Calomino, Ismael
author_facet Calomino, Ismael
Lewis Smith, Andrew
Pelaitay, Gustavo Andrés
author_role author
author2 Lewis Smith, Andrew
Pelaitay, Gustavo Andrés
author2_role author
author
dc.subject.none.fl_str_mv Monadic Pseudocomplemented Distributive Lattices
KALMAN CONSTRUCTION
MONADIC KAN-ALGEBRAS
topic Monadic Pseudocomplemented Distributive Lattices
KALMAN CONSTRUCTION
MONADIC KAN-ALGEBRAS
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 this paper, we study the variety of pseudocomplemented distributive lattices with existential and universal quantifiers, called monadic pseudocomplemented distributive lattices. We introduce the variety of monadic KANalgebras, which turns out to be different from the class studied in [Gomez C., Marcos M., San Martín H.J.: On the relation of negations in Nelson algebras. Rep. Math. Logic 56 (2021), 15–56], and prove that the category of monadic pseudocomplemented distributive lattices is equivalent to the category of centered monadic KAN-algebras, extending the results given in [Calomino I., Pelaitay G.: A new categorical equivalence for Stone algebras. Accepted in Mathematica Slovaca (2025)]
Fil: Calomino, Ismael. Universidad Católica de Ávila; España
Fil: Lewis Smith, Andrew. Middlesex University; Reino Unido
Fil: Pelaitay, Gustavo Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; Argentina. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Instituto de Ciencias Básicas; Argentina
description In this paper, we study the variety of pseudocomplemented distributive lattices with existential and universal quantifiers, called monadic pseudocomplemented distributive lattices. We introduce the variety of monadic KANalgebras, which turns out to be different from the class studied in [Gomez C., Marcos M., San Martín H.J.: On the relation of negations in Nelson algebras. Rep. Math. Logic 56 (2021), 15–56], and prove that the category of monadic pseudocomplemented distributive lattices is equivalent to the category of centered monadic KAN-algebras, extending the results given in [Calomino I., Pelaitay G.: A new categorical equivalence for Stone algebras. Accepted in Mathematica Slovaca (2025)]
publishDate 2025
dc.date.none.fl_str_mv 2025-12
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/11336/281009
Calomino, Ismael; Lewis Smith, Andrew; Pelaitay, Gustavo Andrés; Monadic Pseudocomplemented Distributive Lattices; College Publications; Journal of Applied Logics; 12; 7; 12-2025; 2009-2036
2631-9810
2631-9829
CONICET Digital
CONICET
url http://hdl.handle.net/11336/281009
identifier_str_mv Calomino, Ismael; Lewis Smith, Andrew; Pelaitay, Gustavo Andrés; Monadic Pseudocomplemented Distributive Lattices; College Publications; Journal of Applied Logics; 12; 7; 12-2025; 2009-2036
2631-9810
2631-9829
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://www.collegepublications.co.uk/ifcolog/?00075
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 College Publications
publisher.none.fl_str_mv College Publications
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 13.176822

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