On Some Compatible Operations on Heyting Algebras
- Autores
- Ertola Biraben, Rodolfo Cristian; San Martín, Hernán Javier
- Año de publicación
- 2011
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- We study some operations that may be defined using the minimum operator in the context of a Heyting algebra. Our motivation comes from the fact that 1) already known compatible operations, such as the successor by Kuznetsov, the minimum dense by Smetanich and the operation G by Gabbay may be defined in this way, though almost never explicitly noted in the literature; 2) defining operations in this way is equivalent, from a logical point of view, to two clauses, one corresponding to an introduction rule and the other to an elimination rule, thus providing a manageable way to deal with these operations. Our main result is negative: all operations that arise turn out to be Heyting terms or the mentioned already known operations or operations interdefinable with them. However, it should be noted that some of the operations that arise may exist even if the known operations do not. We also study the extension of Priestley duality to Heyting algebras enriched with the new operations.
Fil: Ertola Biraben, Rodolfo Cristian. Universidad Nacional de La Plata. Facultad de Humanidades y Ciencias de la Educación; Argentina. - Fuente
- Studia Logica, 29(3), 331-345. (2011)
ISSN 0039-3215 - Materia
-
Filosofía
Intuitionistic logic
Heyting algebra
Compatible operation - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/4.0/
- Repositorio
- Institución
- Universidad Nacional de La Plata. Facultad de Humanidades y Ciencias de la Educación
- OAI Identificador
- oai:memoria.fahce.unlp.edu.ar:snrd:Jpr16921
Ver los metadatos del registro completo
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On Some Compatible Operations on Heyting AlgebrasErtola Biraben, Rodolfo CristianSan Martín, Hernán JavierFilosofíaIntuitionistic logicHeyting algebraCompatible operationWe study some operations that may be defined using the minimum operator in the context of a Heyting algebra. Our motivation comes from the fact that 1) already known compatible operations, such as the successor by Kuznetsov, the minimum dense by Smetanich and the operation G by Gabbay may be defined in this way, though almost never explicitly noted in the literature; 2) defining operations in this way is equivalent, from a logical point of view, to two clauses, one corresponding to an introduction rule and the other to an elimination rule, thus providing a manageable way to deal with these operations. Our main result is negative: all operations that arise turn out to be Heyting terms or the mentioned already known operations or operations interdefinable with them. However, it should be noted that some of the operations that arise may exist even if the known operations do not. We also study the extension of Priestley duality to Heyting algebras enriched with the new operations.Fil: Ertola Biraben, Rodolfo Cristian. Universidad Nacional de La Plata. Facultad de Humanidades y Ciencias de la Educación; Argentina.2011info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttps://www.memoria.fahce.unlp.edu.ar/art_revistas/pr.16921/pr.16921.pdfStudia Logica, 29(3), 331-345. (2011)ISSN 0039-3215reponame:Memoria Académica (UNLP-FAHCE)instname:Universidad Nacional de La Plata. Facultad de Humanidades y Ciencias de la Educacióninstacron:UNLPenginfo:eu-repo/semantics/altIdentifier/hdl/10915/137724info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/4.0/2025-09-29T11:57:58Zoai:memoria.fahce.unlp.edu.ar:snrd:Jpr16921Institucionalhttps://www.memoria.fahce.unlp.edu.ar/Universidad públicahttps://www.fahce.unlp.edu.ar/https://www.memoria.fahce.unlp.edu.ar/oaiserver.cgimemoria@fahce.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13412025-09-29 11:57:59.336Memoria Académica (UNLP-FAHCE) - Universidad Nacional de La Plata. Facultad de Humanidades y Ciencias de la Educaciónfalse |
dc.title.none.fl_str_mv |
On Some Compatible Operations on Heyting Algebras |
title |
On Some Compatible Operations on Heyting Algebras |
spellingShingle |
On Some Compatible Operations on Heyting Algebras Ertola Biraben, Rodolfo Cristian Filosofía Intuitionistic logic Heyting algebra Compatible operation |
title_short |
On Some Compatible Operations on Heyting Algebras |
title_full |
On Some Compatible Operations on Heyting Algebras |
title_fullStr |
On Some Compatible Operations on Heyting Algebras |
title_full_unstemmed |
On Some Compatible Operations on Heyting Algebras |
title_sort |
On Some Compatible Operations on Heyting Algebras |
dc.creator.none.fl_str_mv |
Ertola Biraben, Rodolfo Cristian San Martín, Hernán Javier |
author |
Ertola Biraben, Rodolfo Cristian |
author_facet |
Ertola Biraben, Rodolfo Cristian San Martín, Hernán Javier |
author_role |
author |
author2 |
San Martín, Hernán Javier |
author2_role |
author |
dc.subject.none.fl_str_mv |
Filosofía Intuitionistic logic Heyting algebra Compatible operation |
topic |
Filosofía Intuitionistic logic Heyting algebra Compatible operation |
dc.description.none.fl_txt_mv |
We study some operations that may be defined using the minimum operator in the context of a Heyting algebra. Our motivation comes from the fact that 1) already known compatible operations, such as the successor by Kuznetsov, the minimum dense by Smetanich and the operation G by Gabbay may be defined in this way, though almost never explicitly noted in the literature; 2) defining operations in this way is equivalent, from a logical point of view, to two clauses, one corresponding to an introduction rule and the other to an elimination rule, thus providing a manageable way to deal with these operations. Our main result is negative: all operations that arise turn out to be Heyting terms or the mentioned already known operations or operations interdefinable with them. However, it should be noted that some of the operations that arise may exist even if the known operations do not. We also study the extension of Priestley duality to Heyting algebras enriched with the new operations. Fil: Ertola Biraben, Rodolfo Cristian. Universidad Nacional de La Plata. Facultad de Humanidades y Ciencias de la Educación; Argentina. |
description |
We study some operations that may be defined using the minimum operator in the context of a Heyting algebra. Our motivation comes from the fact that 1) already known compatible operations, such as the successor by Kuznetsov, the minimum dense by Smetanich and the operation G by Gabbay may be defined in this way, though almost never explicitly noted in the literature; 2) defining operations in this way is equivalent, from a logical point of view, to two clauses, one corresponding to an introduction rule and the other to an elimination rule, thus providing a manageable way to deal with these operations. Our main result is negative: all operations that arise turn out to be Heyting terms or the mentioned already known operations or operations interdefinable with them. However, it should be noted that some of the operations that arise may exist even if the known operations do not. We also study the extension of Priestley duality to Heyting algebras enriched with the new operations. |
publishDate |
2011 |
dc.date.none.fl_str_mv |
2011 |
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 |
https://www.memoria.fahce.unlp.edu.ar/art_revistas/pr.16921/pr.16921.pdf |
url |
https://www.memoria.fahce.unlp.edu.ar/art_revistas/pr.16921/pr.16921.pdf |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/hdl/10915/137724 |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-sa/4.0/ |
eu_rights_str_mv |
openAccess |
rights_invalid_str_mv |
https://creativecommons.org/licenses/by-nc-sa/4.0/ |
dc.format.none.fl_str_mv |
application/pdf |
dc.source.none.fl_str_mv |
Studia Logica, 29(3), 331-345. (2011) ISSN 0039-3215 reponame:Memoria Académica (UNLP-FAHCE) instname:Universidad Nacional de La Plata. Facultad de Humanidades y Ciencias de la Educación instacron:UNLP |
reponame_str |
Memoria Académica (UNLP-FAHCE) |
collection |
Memoria Académica (UNLP-FAHCE) |
instname_str |
Universidad Nacional de La Plata. Facultad de Humanidades y Ciencias de la Educación |
instacron_str |
UNLP |
institution |
UNLP |
repository.name.fl_str_mv |
Memoria Académica (UNLP-FAHCE) - Universidad Nacional de La Plata. Facultad de Humanidades y Ciencias de la Educación |
repository.mail.fl_str_mv |
memoria@fahce.unlp.edu.ar |
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13.070432 |