Free Łukasiewicz implication algebras

Autores
Díaz Varela, José Patricio
Año de publicación
2008
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Łukasiewicz implication algebras are the {→,1}-subreducts of MV- algebras. They are the algebraic counterpart of Super-Łukasiewicz Implicational Logics investigated in Komori (Nogoya Math J 72:127-133, 1978). In this paper we give a description of free Łukasiewicz implication algebras in the context of McNaughton functions. More precisely, we show that the |X|-free Łukasiewicz implication algebra is isomorphic to ∪x∈X} [xθ) for a certain congruence θ over the |X|-free MV-algebra. As corollary we describe the free algebras in all subvarieties of Łukasiewicz implication algebras.
Fil: Díaz Varela, José Patricio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
Materia
ŁUKASIEWICZ IMPLICATION ALGEBRAS
FREE ALGEBRAS
MCNAUGHTON FUNCTIONS
MV-ALGEBRAS
WAJSBERG 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:11336/95369
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/95369
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Free Łukasiewicz implication algebrasDíaz Varela, José PatricioŁUKASIEWICZ IMPLICATION ALGEBRASFREE ALGEBRASMCNAUGHTON FUNCTIONSMV-ALGEBRASWAJSBERG ALGEBRAShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Łukasiewicz implication algebras are the {→,1}-subreducts of MV- algebras. They are the algebraic counterpart of Super-Łukasiewicz Implicational Logics investigated in Komori (Nogoya Math J 72:127-133, 1978). In this paper we give a description of free Łukasiewicz implication algebras in the context of McNaughton functions. More precisely, we show that the |X|-free Łukasiewicz implication algebra is isomorphic to ∪x∈X} [xθ) for a certain congruence θ over the |X|-free MV-algebra. As corollary we describe the free algebras in all subvarieties of Łukasiewicz implication algebras.Fil: Díaz Varela, José Patricio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaSpringer2008-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/95369Díaz Varela, José Patricio; Free Łukasiewicz implication algebras; Springer; Archive for Mathematical Logic - (Print); 47; 1; 6-2008; 25-330933-5846CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00153-008-0067-5info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00153-008-0067-5#article-infoinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-05T10:19:03Zoai:ri.conicet.gov.ar:11336/95369instacron: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:34982025-11-05 10:19:03.977CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Free Łukasiewicz implication algebras
title Free Łukasiewicz implication algebras
spellingShingle Free Łukasiewicz implication algebras
Díaz Varela, José Patricio
ŁUKASIEWICZ IMPLICATION ALGEBRAS
FREE ALGEBRAS
MCNAUGHTON FUNCTIONS
MV-ALGEBRAS
WAJSBERG ALGEBRAS
title_short Free Łukasiewicz implication algebras
title_full Free Łukasiewicz implication algebras
title_fullStr Free Łukasiewicz implication algebras
title_full_unstemmed Free Łukasiewicz implication algebras
title_sort Free Łukasiewicz implication algebras
dc.creator.none.fl_str_mv Díaz Varela, José Patricio
author Díaz Varela, José Patricio
author_facet Díaz Varela, José Patricio
author_role author
dc.subject.none.fl_str_mv ŁUKASIEWICZ IMPLICATION ALGEBRAS
FREE ALGEBRAS
MCNAUGHTON FUNCTIONS
MV-ALGEBRAS
WAJSBERG ALGEBRAS
topic ŁUKASIEWICZ IMPLICATION ALGEBRAS
FREE ALGEBRAS
MCNAUGHTON FUNCTIONS
MV-ALGEBRAS
WAJSBERG 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 Łukasiewicz implication algebras are the {→,1}-subreducts of MV- algebras. They are the algebraic counterpart of Super-Łukasiewicz Implicational Logics investigated in Komori (Nogoya Math J 72:127-133, 1978). In this paper we give a description of free Łukasiewicz implication algebras in the context of McNaughton functions. More precisely, we show that the |X|-free Łukasiewicz implication algebra is isomorphic to ∪x∈X} [xθ) for a certain congruence θ over the |X|-free MV-algebra. As corollary we describe the free algebras in all subvarieties of Łukasiewicz implication algebras.
Fil: Díaz Varela, José Patricio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
description Łukasiewicz implication algebras are the {→,1}-subreducts of MV- algebras. They are the algebraic counterpart of Super-Łukasiewicz Implicational Logics investigated in Komori (Nogoya Math J 72:127-133, 1978). In this paper we give a description of free Łukasiewicz implication algebras in the context of McNaughton functions. More precisely, we show that the |X|-free Łukasiewicz implication algebra is isomorphic to ∪x∈X} [xθ) for a certain congruence θ over the |X|-free MV-algebra. As corollary we describe the free algebras in all subvarieties of Łukasiewicz implication algebras.
publishDate 2008
dc.date.none.fl_str_mv 2008-06
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/11336/95369
Díaz Varela, José Patricio; Free Łukasiewicz implication algebras; Springer; Archive for Mathematical Logic - (Print); 47; 1; 6-2008; 25-33
0933-5846
CONICET Digital
CONICET
url http://hdl.handle.net/11336/95369
identifier_str_mv Díaz Varela, José Patricio; Free Łukasiewicz implication algebras; Springer; Archive for Mathematical Logic - (Print); 47; 1; 6-2008; 25-33
0933-5846
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s00153-008-0067-5
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00153-008-0067-5#article-info
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 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 13.087074

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