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
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/164538
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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. |
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2019 |
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2019-06 |
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