Compatible operations on commutative weak residuated lattices

Autores
San Martín, Hernán Javier
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Compatibility of functions is a classical topic in Universal Algebra related to the notion of affine completeness. In algebraic logic, it is concerned with the possibility of implicitly defining new connectives. In this paper, we give characterizations of compatible operations in a variety of algebras that properly includes commutative residuated lattices and some generalizations of Heyting algebras. The wider variety considered is obtained by weakening the main characters of residuated lattices (A, ∧, ∨, ·, →, e) but retaining most of their algebraic consequences, and their algebras have a commutative monoidal structure. The order-extension principle a ≤ b if and only if a → b ≥ e is replaced by the condition: if a ≤ b, then a → b ≥ e. The residuation property c ≤ a → b if and only if a · c ≤ b is replaced by the conditions: if c ≤ a → b , then a · c ≤ b, and if a · c ≤ b, then e → c ≤ a → b. Some further algebraic conditions of commutative residuated lattices are required.
Facultad de Ciencias Exactas
Materia
Matemática
commutative residuated lattices
weak Heyting algebras
congruences
compatible functions
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/139191

id SEDICI_0cfe90432c84841c451c8dfcd6929a7c
oai_identifier_str oai:sedici.unlp.edu.ar:10915/139191
network_acronym_str SEDICI
repository_id_str 1329
network_name_str SEDICI (UNLP)
spelling Compatible operations on commutative weak residuated latticesSan Martín, Hernán JavierMatemáticacommutative residuated latticesweak Heyting algebrascongruencescompatible functionsCompatibility of functions is a classical topic in Universal Algebra related to the notion of affine completeness. In algebraic logic, it is concerned with the possibility of implicitly defining new connectives. In this paper, we give characterizations of compatible operations in a variety of algebras that properly includes commutative residuated lattices and some generalizations of Heyting algebras. The wider variety considered is obtained by weakening the main characters of residuated lattices (A, ∧, ∨, ·, →, e) but retaining most of their algebraic consequences, and their algebras have a commutative monoidal structure. The order-extension principle a ≤ b if and only if a → b ≥ e is replaced by the condition: if a ≤ b, then a → b ≥ e. The residuation property c ≤ a → b if and only if a · c ≤ b is replaced by the conditions: if c ≤ a → b , then a · c ≤ b, and if a · c ≤ b, then e → c ≤ a → b. Some further algebraic conditions of commutative residuated lattices are required.Facultad de Ciencias Exactas2015-02-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf143-155http://sedici.unlp.edu.ar/handle/10915/139191enginfo:eu-repo/semantics/altIdentifier/issn/0002-5240info:eu-repo/semantics/altIdentifier/issn/1420-8911info:eu-repo/semantics/altIdentifier/doi/10.1007/s00012-015-0317-4info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/4.0/Creative Commons Attribution 4.0 International (CC BY 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-03T11:04:04Zoai:sedici.unlp.edu.ar:10915/139191Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-03 11:04:04.706SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Compatible operations on commutative weak residuated lattices
title Compatible operations on commutative weak residuated lattices
spellingShingle Compatible operations on commutative weak residuated lattices
San Martín, Hernán Javier
Matemática
commutative residuated lattices
weak Heyting algebras
congruences
compatible functions
title_short Compatible operations on commutative weak residuated lattices
title_full Compatible operations on commutative weak residuated lattices
title_fullStr Compatible operations on commutative weak residuated lattices
title_full_unstemmed Compatible operations on commutative weak residuated lattices
title_sort Compatible operations on commutative weak residuated lattices
dc.creator.none.fl_str_mv San Martín, Hernán Javier
author San Martín, Hernán Javier
author_facet San Martín, Hernán Javier
author_role author
dc.subject.none.fl_str_mv Matemática
commutative residuated lattices
weak Heyting algebras
congruences
compatible functions
topic Matemática
commutative residuated lattices
weak Heyting algebras
congruences
compatible functions
dc.description.none.fl_txt_mv Compatibility of functions is a classical topic in Universal Algebra related to the notion of affine completeness. In algebraic logic, it is concerned with the possibility of implicitly defining new connectives. In this paper, we give characterizations of compatible operations in a variety of algebras that properly includes commutative residuated lattices and some generalizations of Heyting algebras. The wider variety considered is obtained by weakening the main characters of residuated lattices (A, ∧, ∨, ·, →, e) but retaining most of their algebraic consequences, and their algebras have a commutative monoidal structure. The order-extension principle a ≤ b if and only if a → b ≥ e is replaced by the condition: if a ≤ b, then a → b ≥ e. The residuation property c ≤ a → b if and only if a · c ≤ b is replaced by the conditions: if c ≤ a → b , then a · c ≤ b, and if a · c ≤ b, then e → c ≤ a → b. Some further algebraic conditions of commutative residuated lattices are required.
Facultad de Ciencias Exactas
description Compatibility of functions is a classical topic in Universal Algebra related to the notion of affine completeness. In algebraic logic, it is concerned with the possibility of implicitly defining new connectives. In this paper, we give characterizations of compatible operations in a variety of algebras that properly includes commutative residuated lattices and some generalizations of Heyting algebras. The wider variety considered is obtained by weakening the main characters of residuated lattices (A, ∧, ∨, ·, →, e) but retaining most of their algebraic consequences, and their algebras have a commutative monoidal structure. The order-extension principle a ≤ b if and only if a → b ≥ e is replaced by the condition: if a ≤ b, then a → b ≥ e. The residuation property c ≤ a → b if and only if a · c ≤ b is replaced by the conditions: if c ≤ a → b , then a · c ≤ b, and if a · c ≤ b, then e → c ≤ a → b. Some further algebraic conditions of commutative residuated lattices are required.
publishDate 2015
dc.date.none.fl_str_mv 2015-02-05
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
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://sedici.unlp.edu.ar/handle/10915/139191
url http://sedici.unlp.edu.ar/handle/10915/139191
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/0002-5240
info:eu-repo/semantics/altIdentifier/issn/1420-8911
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00012-015-0317-4
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/4.0/
Creative Commons Attribution 4.0 International (CC BY 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/4.0/
Creative Commons Attribution 4.0 International (CC BY 4.0)
dc.format.none.fl_str_mv application/pdf
143-155
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_ 1842260539417296896
score 13.13397