Discrete duality for 3-valued Lukasiewicz-Moisil algebras
- Autores
- Pelaitay, Gustavo Andrés
- Año de publicación
- 2017
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- In 2011, Düntsch and Orlowska obtained a discrete duality for regular double Stone algebras. On the other hand, it is well known that regular double Stone algebras are polinominally equivalent to 3-valued Lukasiewicz-Moisil algebras (or LM3-algebras). In [R. Cignoli, Injective De Morgan and Kleene algebra, Proc. Amer. Math. Soc. 47 (1975) 269-278], LM3-algebras are considered as a Kleene algebras (L,∨,∧,∼, 0, 1) endowed with a unary operation : L → L, satisfying the properties: a∨ ∼ a = 1, ∼ a ∧ a = a∧ ∼ a and a∨b ≤(a ∨ b). Motivated by this result, in this paper, we determine another discrete duality for LM3-algebras, extending the discrete duality to De Morgan algebras described in [W. Dzik, E. Orlowska and C. van Alten, Relational representation theorems for general lattices with negations, in Relations and Kleene Algebra in Computer Science, Lecture Notes in Computer Science, Vol. 4136 (Springer, Berlin, 2006), pp. 162-176].
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; Argentina - Materia
-
3 -VALUED LUKASIEWICZ-MOISIL ALGEBRAS
DE MORGAN ALGEBRAS
DISCRETE DUALITY - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
.jpg)
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/97231
Ver los metadatos del registro completo
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Discrete duality for 3-valued Lukasiewicz-Moisil algebrasPelaitay, Gustavo Andrés3 -VALUED LUKASIEWICZ-MOISIL ALGEBRASDE MORGAN ALGEBRASDISCRETE DUALITYhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In 2011, Düntsch and Orlowska obtained a discrete duality for regular double Stone algebras. On the other hand, it is well known that regular double Stone algebras are polinominally equivalent to 3-valued Lukasiewicz-Moisil algebras (or LM3-algebras). In [R. Cignoli, Injective De Morgan and Kleene algebra, Proc. Amer. Math. Soc. 47 (1975) 269-278], LM3-algebras are considered as a Kleene algebras (L,∨,∧,∼, 0, 1) endowed with a unary operation : L → L, satisfying the properties: a∨ ∼ a = 1, ∼ a ∧ a = a∧ ∼ a and a∨b ≤(a ∨ b). Motivated by this result, in this paper, we determine another discrete duality for LM3-algebras, extending the discrete duality to De Morgan algebras described in [W. Dzik, E. Orlowska and C. van Alten, Relational representation theorems for general lattices with negations, in Relations and Kleene Algebra in Computer Science, Lecture Notes in Computer Science, Vol. 4136 (Springer, Berlin, 2006), pp. 162-176].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; ArgentinaWorld Scientific Publishing2017-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/97231Pelaitay, Gustavo Andrés; Discrete duality for 3-valued Lukasiewicz-Moisil algebras; World Scientific Publishing; Asian-European Journal of Mathematics; 10; 1; 3-2017; 1-61793-7183CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1142/S1793557117500036info:eu-repo/semantics/altIdentifier/url/https://www.worldscientific.com/doi/abs/10.1142/S1793557117500036info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:49:03Zoai:ri.conicet.gov.ar:11336/97231instacron: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 09:49:03.916CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
| dc.title.none.fl_str_mv |
Discrete duality for 3-valued Lukasiewicz-Moisil algebras |
| title |
Discrete duality for 3-valued Lukasiewicz-Moisil algebras |
| spellingShingle |
Discrete duality for 3-valued Lukasiewicz-Moisil algebras Pelaitay, Gustavo Andrés 3 -VALUED LUKASIEWICZ-MOISIL ALGEBRAS DE MORGAN ALGEBRAS DISCRETE DUALITY |
| title_short |
Discrete duality for 3-valued Lukasiewicz-Moisil algebras |
| title_full |
Discrete duality for 3-valued Lukasiewicz-Moisil algebras |
| title_fullStr |
Discrete duality for 3-valued Lukasiewicz-Moisil algebras |
| title_full_unstemmed |
Discrete duality for 3-valued Lukasiewicz-Moisil algebras |
| title_sort |
Discrete duality for 3-valued Lukasiewicz-Moisil algebras |
| dc.creator.none.fl_str_mv |
Pelaitay, Gustavo Andrés |
| author |
Pelaitay, Gustavo Andrés |
| author_facet |
Pelaitay, Gustavo Andrés |
| author_role |
author |
| dc.subject.none.fl_str_mv |
3 -VALUED LUKASIEWICZ-MOISIL ALGEBRAS DE MORGAN ALGEBRAS DISCRETE DUALITY |
| topic |
3 -VALUED LUKASIEWICZ-MOISIL ALGEBRAS DE MORGAN ALGEBRAS DISCRETE DUALITY |
| 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 2011, Düntsch and Orlowska obtained a discrete duality for regular double Stone algebras. On the other hand, it is well known that regular double Stone algebras are polinominally equivalent to 3-valued Lukasiewicz-Moisil algebras (or LM3-algebras). In [R. Cignoli, Injective De Morgan and Kleene algebra, Proc. Amer. Math. Soc. 47 (1975) 269-278], LM3-algebras are considered as a Kleene algebras (L,∨,∧,∼, 0, 1) endowed with a unary operation : L → L, satisfying the properties: a∨ ∼ a = 1, ∼ a ∧ a = a∧ ∼ a and a∨b ≤(a ∨ b). Motivated by this result, in this paper, we determine another discrete duality for LM3-algebras, extending the discrete duality to De Morgan algebras described in [W. Dzik, E. Orlowska and C. van Alten, Relational representation theorems for general lattices with negations, in Relations and Kleene Algebra in Computer Science, Lecture Notes in Computer Science, Vol. 4136 (Springer, Berlin, 2006), pp. 162-176]. 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; Argentina |
| description |
In 2011, Düntsch and Orlowska obtained a discrete duality for regular double Stone algebras. On the other hand, it is well known that regular double Stone algebras are polinominally equivalent to 3-valued Lukasiewicz-Moisil algebras (or LM3-algebras). In [R. Cignoli, Injective De Morgan and Kleene algebra, Proc. Amer. Math. Soc. 47 (1975) 269-278], LM3-algebras are considered as a Kleene algebras (L,∨,∧,∼, 0, 1) endowed with a unary operation : L → L, satisfying the properties: a∨ ∼ a = 1, ∼ a ∧ a = a∧ ∼ a and a∨b ≤(a ∨ b). Motivated by this result, in this paper, we determine another discrete duality for LM3-algebras, extending the discrete duality to De Morgan algebras described in [W. Dzik, E. Orlowska and C. van Alten, Relational representation theorems for general lattices with negations, in Relations and Kleene Algebra in Computer Science, Lecture Notes in Computer Science, Vol. 4136 (Springer, Berlin, 2006), pp. 162-176]. |
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2017 |
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2017-03 |
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info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
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article |
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publishedVersion |
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http://hdl.handle.net/11336/97231 Pelaitay, Gustavo Andrés; Discrete duality for 3-valued Lukasiewicz-Moisil algebras; World Scientific Publishing; Asian-European Journal of Mathematics; 10; 1; 3-2017; 1-6 1793-7183 CONICET Digital CONICET |
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http://hdl.handle.net/11336/97231 |
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Pelaitay, Gustavo Andrés; Discrete duality for 3-valued Lukasiewicz-Moisil algebras; World Scientific Publishing; Asian-European Journal of Mathematics; 10; 1; 3-2017; 1-6 1793-7183 CONICET Digital CONICET |
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eng |
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eng |
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info:eu-repo/semantics/altIdentifier/doi/10.1142/S1793557117500036 info:eu-repo/semantics/altIdentifier/url/https://www.worldscientific.com/doi/abs/10.1142/S1793557117500036 |
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World Scientific Publishing |
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