Geometry of Robinson consistency in Łukasiewicz logic

We establish the Robinson joint consistency theorem for the infinite-valued propositional logic of Łukasiewicz. As a corollary we easily obtain the amalgamation property for MV-algebras-the algebras of Łukasiewicz logic: all pre-existing proofs of this latter result make essential use of the Pierce...

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Detalles Bibliográficos
Autores: Busaniche, Manuela, Mundici, Daniele
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2007
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/84081
Acceso en línea:http://hdl.handle.net/11336/84081
Access Level:acceso abierto
Palabra clave:ŁUkasiewicz&Nbsp;Logic
Amalgamation
Finite-Valued Logic
Free Mv-Algebra
Infinite-Valued Logic
Krull Depth
Mcnaughton Function
Mv-Algebra
Prime Ideal
Robinson Joint Consistency
Unimodular Triangulation
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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spelling Geometry of Robinson consistency in Łukasiewicz logicBusaniche, ManuelaMundici, DanieleŁUkasiewicz&Nbsp;LogicAmalgamationFinite-Valued LogicFree Mv-AlgebraInfinite-Valued LogicKrull DepthMcnaughton FunctionMv-AlgebraPrime IdealRobinson Joint ConsistencyUnimodular Triangulationhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We establish the Robinson joint consistency theorem for the infinite-valued propositional logic of Łukasiewicz. As a corollary we easily obtain the amalgamation property for MV-algebras-the algebras of Łukasiewicz logic: all pre-existing proofs of this latter result make essential use of the Pierce amalgamation theorem for abelian lattice-ordered groups (with strong unit) together with the categorical equivalence Γ between these groups and MV-algebras. Our main tools are elementary and geometric.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; ArgentinaFil: Mundici, Daniele. Università degli Studi di Firenze; ItaliaElsevier Science2007-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/84081Busaniche, Manuela; Mundici, Daniele; Geometry of Robinson consistency in Łukasiewicz logic; Elsevier Science; Annals Of Pure And Applied Logic; 147; 1-2; 6-2007; 1-220168-0072CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.apal.2006.11.003info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T13:49:05Zoai:ri.conicet.gov.ar:11336/84081instacron: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:34982024-05-08 13:49:05.503CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Geometry of Robinson consistency in Łukasiewicz logic
title Geometry of Robinson consistency in Łukasiewicz logic
spellingShingle Geometry of Robinson consistency in Łukasiewicz logic
Busaniche, Manuela
ŁUkasiewicz&Nbsp;Logic
Amalgamation
Finite-Valued Logic
Free Mv-Algebra
Infinite-Valued Logic
Krull Depth
Mcnaughton Function
Mv-Algebra
Prime Ideal
Robinson Joint Consistency
Unimodular Triangulation
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
title_short Geometry of Robinson consistency in Łukasiewicz logic
title_full Geometry of Robinson consistency in Łukasiewicz logic
title_fullStr Geometry of Robinson consistency in Łukasiewicz logic
title_full_unstemmed Geometry of Robinson consistency in Łukasiewicz logic
title_sort Geometry of Robinson consistency in Łukasiewicz logic
dc.creator.none.fl_str_mv Busaniche, Manuela
Mundici, Daniele
author Busaniche, Manuela
author_facet Busaniche, Manuela
Mundici, Daniele
author_role author
author2 Mundici, Daniele
author2_role author
dc.subject.none.fl_str_mv ŁUkasiewicz&Nbsp;Logic
Amalgamation
Finite-Valued Logic
Free Mv-Algebra
Infinite-Valued Logic
Krull Depth
Mcnaughton Function
Mv-Algebra
Prime Ideal
Robinson Joint Consistency
Unimodular Triangulation
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
topic ŁUkasiewicz&Nbsp;Logic
Amalgamation
Finite-Valued Logic
Free Mv-Algebra
Infinite-Valued Logic
Krull Depth
Mcnaughton Function
Mv-Algebra
Prime Ideal
Robinson Joint Consistency
Unimodular Triangulation
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
description We establish the Robinson joint consistency theorem for the infinite-valued propositional logic of Łukasiewicz. As a corollary we easily obtain the amalgamation property for MV-algebras-the algebras of Łukasiewicz logic: all pre-existing proofs of this latter result make essential use of the Pierce amalgamation theorem for abelian lattice-ordered groups (with strong unit) together with the categorical equivalence Γ between these groups and MV-algebras. Our main tools are elementary and geometric.
publishDate 2007
dc.date.none.fl_str_mv 2007-06
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/11336/84081
Busaniche, Manuela; Mundici, Daniele; Geometry of Robinson consistency in Łukasiewicz logic; Elsevier Science; Annals Of Pure And Applied Logic; 147; 1-2; 6-2007; 1-22
0168-0072
CONICET Digital
CONICET
url http://hdl.handle.net/11336/84081
identifier_str_mv Busaniche, Manuela; Mundici, Daniele; Geometry of Robinson consistency in Łukasiewicz logic; Elsevier Science; Annals Of Pure And Applied Logic; 147; 1-2; 6-2007; 1-22
0168-0072
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.apal.2006.11.003
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 Elsevier Science
publisher.none.fl_str_mv Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
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 15,812429

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