Spectral duality for finitely generated nilpotent minimum algebras, with applications

Autores
Aguzzoli, Stefano; Busaniche, Manuela; Marra, Vincenzo
Año de publicación
2007
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We establish a categorical duality for the finitely generated Lindenbaum-Tarski algebras of prepositional nilpotent minimum logic. The latter's conjunction is semantically interpreted by a left-continuous (but not continuous) triangular norm; implication is obtained through residuation. Our duality allows one to transfer to nilpotent minimum, logic several known results about inutitionistic logic with the prelinearity axiom (also called Gödel-Dummett logic), mutatis mutandis. We give several such applications.
Fil: Aguzzoli, Stefano. Università degli Studi di Milano; Italia
Fil: Busaniche, Manuela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Marra, Vincenzo. Università degli Studi di Milano; Italia
Materia
AMALGAMATION
INTERPOLATION
PRIME SPECTRUM
SPECTRAL DUALITY
T-NORM BASED LOGICS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/84267
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/84267
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Spectral duality for finitely generated nilpotent minimum algebras, with applicationsAguzzoli, StefanoBusaniche, ManuelaMarra, VincenzoAMALGAMATIONINTERPOLATIONPRIME SPECTRUMSPECTRAL DUALITYT-NORM BASED LOGICShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We establish a categorical duality for the finitely generated Lindenbaum-Tarski algebras of prepositional nilpotent minimum logic. The latter's conjunction is semantically interpreted by a left-continuous (but not continuous) triangular norm; implication is obtained through residuation. Our duality allows one to transfer to nilpotent minimum, logic several known results about inutitionistic logic with the prelinearity axiom (also called Gödel-Dummett logic), mutatis mutandis. We give several such applications.Fil: Aguzzoli, Stefano. Università degli Studi di Milano; ItaliaFil: Busaniche, Manuela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Marra, Vincenzo. Università degli Studi di Milano; ItaliaOxford University Press2007-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/84267Aguzzoli, Stefano; Busaniche, Manuela; Marra, Vincenzo; Spectral duality for finitely generated nilpotent minimum algebras, with applications; Oxford University Press; Journal of Logic and Computation; 17; 4; 8-2007; 749-7650955-792XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1093/logcom/exm021info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:43:54Zoai:ri.conicet.gov.ar:11336/84267instacron: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 09:43:54.463CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Spectral duality for finitely generated nilpotent minimum algebras, with applications
title Spectral duality for finitely generated nilpotent minimum algebras, with applications
spellingShingle Spectral duality for finitely generated nilpotent minimum algebras, with applications
Aguzzoli, Stefano
AMALGAMATION
INTERPOLATION
PRIME SPECTRUM
SPECTRAL DUALITY
T-NORM BASED LOGICS
title_short Spectral duality for finitely generated nilpotent minimum algebras, with applications
title_full Spectral duality for finitely generated nilpotent minimum algebras, with applications
title_fullStr Spectral duality for finitely generated nilpotent minimum algebras, with applications
title_full_unstemmed Spectral duality for finitely generated nilpotent minimum algebras, with applications
title_sort Spectral duality for finitely generated nilpotent minimum algebras, with applications
dc.creator.none.fl_str_mv Aguzzoli, Stefano
Busaniche, Manuela
Marra, Vincenzo
author Aguzzoli, Stefano
author_facet Aguzzoli, Stefano
Busaniche, Manuela
Marra, Vincenzo
author_role author
author2 Busaniche, Manuela
Marra, Vincenzo
author2_role author
author
dc.subject.none.fl_str_mv AMALGAMATION
INTERPOLATION
PRIME SPECTRUM
SPECTRAL DUALITY
T-NORM BASED LOGICS
topic AMALGAMATION
INTERPOLATION
PRIME SPECTRUM
SPECTRAL DUALITY
T-NORM BASED LOGICS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We establish a categorical duality for the finitely generated Lindenbaum-Tarski algebras of prepositional nilpotent minimum logic. The latter's conjunction is semantically interpreted by a left-continuous (but not continuous) triangular norm; implication is obtained through residuation. Our duality allows one to transfer to nilpotent minimum, logic several known results about inutitionistic logic with the prelinearity axiom (also called Gödel-Dummett logic), mutatis mutandis. We give several such applications.
Fil: Aguzzoli, Stefano. Università degli Studi di Milano; Italia
Fil: Busaniche, Manuela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Marra, Vincenzo. Università degli Studi di Milano; Italia
description We establish a categorical duality for the finitely generated Lindenbaum-Tarski algebras of prepositional nilpotent minimum logic. The latter's conjunction is semantically interpreted by a left-continuous (but not continuous) triangular norm; implication is obtained through residuation. Our duality allows one to transfer to nilpotent minimum, logic several known results about inutitionistic logic with the prelinearity axiom (also called Gödel-Dummett logic), mutatis mutandis. We give several such applications.
publishDate 2007
dc.date.none.fl_str_mv 2007-08
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 http://hdl.handle.net/11336/84267
Aguzzoli, Stefano; Busaniche, Manuela; Marra, Vincenzo; Spectral duality for finitely generated nilpotent minimum algebras, with applications; Oxford University Press; Journal of Logic and Computation; 17; 4; 8-2007; 749-765
0955-792X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/84267
identifier_str_mv Aguzzoli, Stefano; Busaniche, Manuela; Marra, Vincenzo; Spectral duality for finitely generated nilpotent minimum algebras, with applications; Oxford University Press; Journal of Logic and Computation; 17; 4; 8-2007; 749-765
0955-792X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1093/logcom/exm021
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Oxford University Press
publisher.none.fl_str_mv Oxford University Press
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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