El reticulado de subvariedades de MG

Autores
Díaz Varela, Patricio; Lubomirsky, Noemí
Año de publicación
2019
Idioma
español castellano
Tipo de recurso
documento de conferencia
Estado
versión publicada
Descripción
Contenido: - T-normas. - Hoops y BL-algebras. - Subvariedad MG. - Λ(MG). - Bases ecuacionales. - Álgebras libres. - Bibliografía.
BL-algebras were introduced by Hájek (see [5]) to formalize fuzzy logics in which the conjunction is interpreted by continuous t-norms over the real interval [0;1]. These algebras form a variety, usually called BL. In this work we will concentrate in the subvariety MG ⊆ BL generated by the ordinal sum of the algebra [0;1]MV and the Gödel hoop [0;1]G, that is, generated by A = [0;1]MV ⊕ [0;1]G. Though it is well-known that [0;1]G is decomposable as an infinite ordinal sum of two-elements Boolean algebra, the idea is to treat it as a whole block. The elements of this block are the dense elements of the generating chain and the elements in [0;1]MV are usually called regular elements of A: The main advantage of this approach, is that unlike the work done in [3] and [1], when the number n of generators of the free algebra increase the generating chain remains fixed. This provides a clear insight of the role of the two main blocks of the generating chain in the description of the functions in the free algebra: the role of the regular elements and the role of the dense elements. We have a functional representation for the free algebra FreeMG (n). To define this functions we need to decompose the domain Aⁿ = ([0;1]MV ⊕ [0;1]G)ⁿ in a finite number of pieces. In each piece a function F ∈ FreeMG (n) coincides either with McNaughton functions or functions of FreeG (n). Using [2] and [4] we give a description of the elements in the lattice of subvarieties of the variety MG and the equational characterization of them.
Facultad de Ciencias Exactas
Departamento de Matemática
Materia
Ciencias Exactas
Matemática
Álgebra
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/164538

id SEDICI_417bf14071d8f08895b482aab091a048
oai_identifier_str oai:sedici.unlp.edu.ar:10915/164538
network_acronym_str SEDICI
repository_id_str 1329
network_name_str SEDICI (UNLP)
spelling El reticulado de subvariedades de MGThe lattice of subvarieties of the variety MGDíaz Varela, PatricioLubomirsky, NoemíCiencias ExactasMatemáticaÁlgebraContenido: - T-normas. - Hoops y BL-algebras. - Subvariedad MG. - Λ(MG). - Bases ecuacionales. - Álgebras libres. - Bibliografía.BL-algebras were introduced by Hájek (see [5]) to formalize fuzzy logics in which the conjunction is interpreted by continuous t-norms over the real interval [0;1]. These algebras form a variety, usually called BL. In this work we will concentrate in the subvariety MG ⊆ BL generated by the ordinal sum of the algebra [0;1]MV and the Gödel hoop [0;1]G, that is, generated by A = [0;1]MV ⊕ [0;1]G. Though it is well-known that [0;1]G is decomposable as an infinite ordinal sum of two-elements Boolean algebra, the idea is to treat it as a whole block. The elements of this block are the dense elements of the generating chain and the elements in [0;1]MV are usually called regular elements of A: The main advantage of this approach, is that unlike the work done in [3] and [1], when the number n of generators of the free algebra increase the generating chain remains fixed. This provides a clear insight of the role of the two main blocks of the generating chain in the description of the functions in the free algebra: the role of the regular elements and the role of the dense elements. We have a functional representation for the free algebra FreeMG (n). To define this functions we need to decompose the domain Aⁿ = ([0;1]MV ⊕ [0;1]G)ⁿ in a finite number of pieces. In each piece a function F ∈ FreeMG (n) coincides either with McNaughton functions or functions of FreeG (n). Using [2] and [4] we give a description of the elements in the lattice of subvarieties of the variety MG and the equational characterization of them.Facultad de Ciencias ExactasDepartamento de Matemática2019-06info:eu-repo/semantics/conferenceObjectinfo:eu-repo/semantics/publishedVersionObjeto de conferenciahttp://purl.org/coar/resource_type/c_5794info:ar-repo/semantics/documentoDeConferenciaapplication/pdfhttp://sedici.unlp.edu.ar/handle/10915/164538spainfo:eu-repo/semantics/altIdentifier/url/https://www.matematica.uns.edu.ar/xvcm/comunicaciones/Logica/Monteiro_Lubomirsky.pdfinfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-29T11:43:36Zoai:sedici.unlp.edu.ar:10915/164538Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:43:37.087SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv El reticulado de subvariedades de MG
The lattice of subvarieties of the variety MG
title El reticulado de subvariedades de MG
spellingShingle El reticulado de subvariedades de MG
Díaz Varela, Patricio
Ciencias Exactas
Matemática
Álgebra
title_short El reticulado de subvariedades de MG
title_full El reticulado de subvariedades de MG
title_fullStr El reticulado de subvariedades de MG
title_full_unstemmed El reticulado de subvariedades de MG
title_sort El reticulado de subvariedades de MG
dc.creator.none.fl_str_mv Díaz Varela, Patricio
Lubomirsky, Noemí
author Díaz Varela, Patricio
author_facet Díaz Varela, Patricio
Lubomirsky, Noemí
author_role author
author2 Lubomirsky, Noemí
author2_role author
dc.subject.none.fl_str_mv Ciencias Exactas
Matemática
Álgebra
topic Ciencias Exactas
Matemática
Álgebra
dc.description.none.fl_txt_mv Contenido: - T-normas. - Hoops y BL-algebras. - Subvariedad MG. - Λ(MG). - Bases ecuacionales. - Álgebras libres. - Bibliografía.
BL-algebras were introduced by Hájek (see [5]) to formalize fuzzy logics in which the conjunction is interpreted by continuous t-norms over the real interval [0;1]. These algebras form a variety, usually called BL. In this work we will concentrate in the subvariety MG ⊆ BL generated by the ordinal sum of the algebra [0;1]MV and the Gödel hoop [0;1]G, that is, generated by A = [0;1]MV ⊕ [0;1]G. Though it is well-known that [0;1]G is decomposable as an infinite ordinal sum of two-elements Boolean algebra, the idea is to treat it as a whole block. The elements of this block are the dense elements of the generating chain and the elements in [0;1]MV are usually called regular elements of A: The main advantage of this approach, is that unlike the work done in [3] and [1], when the number n of generators of the free algebra increase the generating chain remains fixed. This provides a clear insight of the role of the two main blocks of the generating chain in the description of the functions in the free algebra: the role of the regular elements and the role of the dense elements. We have a functional representation for the free algebra FreeMG (n). To define this functions we need to decompose the domain Aⁿ = ([0;1]MV ⊕ [0;1]G)ⁿ in a finite number of pieces. In each piece a function F ∈ FreeMG (n) coincides either with McNaughton functions or functions of FreeG (n). Using [2] and [4] we give a description of the elements in the lattice of subvarieties of the variety MG and the equational characterization of them.
Facultad de Ciencias Exactas
Departamento de Matemática
description Contenido: - T-normas. - Hoops y BL-algebras. - Subvariedad MG. - Λ(MG). - Bases ecuacionales. - Álgebras libres. - Bibliografía.
publishDate 2019
dc.date.none.fl_str_mv 2019-06
dc.type.none.fl_str_mv info:eu-repo/semantics/conferenceObject
info:eu-repo/semantics/publishedVersion
Objeto de conferencia
http://purl.org/coar/resource_type/c_5794
info:ar-repo/semantics/documentoDeConferencia
format conferenceObject
status_str publishedVersion
dc.identifier.none.fl_str_mv http://sedici.unlp.edu.ar/handle/10915/164538
url http://sedici.unlp.edu.ar/handle/10915/164538
dc.language.none.fl_str_mv spa
language spa
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.matematica.uns.edu.ar/xvcm/comunicaciones/Logica/Monteiro_Lubomirsky.pdf
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
_version_ 1844616304341811200
score 13.070432