Putting together Łukasiewicz and product logics

In this paper we investigate a propositional fuzzy logical system $\L\Pi$ which contains the well-known \L ukasiewicz, Product and G\"{o}del fuzzy logics as sublogics. We define the corresponding algebraic structures, called $\L\Pi$-algebras and prove the following completeness result: a formul...

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Detalles Bibliográficos
Autores: Esteva Massaguer, Francesc, Godo Lacasa, Lluís
Tipo de recurso: artículo
Fecha de publicación:1999
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2099/3555
Acceso en línea:https://hdl.handle.net/2099/3555
Access Level:acceso abierto
Palabra clave:Ł∏ algebras
Lògica matemàtica
Classificació AMS::03 Mathematical logic and foundations::03B General logic
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spelling Putting together Łukasiewicz and product logicsEsteva Massaguer, FrancescGodo Lacasa, LluísŁ∏ algebrasLògica matemàticaClassificació AMS::03 Mathematical logic and foundations::03B General logicIn this paper we investigate a propositional fuzzy logical system $\L\Pi$ which contains the well-known \L ukasiewicz, Product and G\"{o}del fuzzy logics as sublogics. We define the corresponding algebraic structures, called $\L\Pi$-algebras and prove the following completeness result: a formula $\varphi$ is provable in the $\L\Pi$ logic iff it is a tautology for all linear $\L\Pi$-algebras. Moreover, linear $\L\Pi$-algebras are shown to be embeddable in linearly ordered abelian rings with a strong unit and cancellation law.Universitat Politècnica de Catalunya. Secció de Matemàtiques i Informàtica19991999-01-0120072007-09-25journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2099/3555reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2http://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2099/35552026-05-27T15:37:01Z
dc.title.none.fl_str_mv Putting together Łukasiewicz and product logics
title Putting together Łukasiewicz and product logics
spellingShingle Putting together Łukasiewicz and product logics
Esteva Massaguer, Francesc
Ł∏ algebras
Lògica matemàtica
Classificació AMS::03 Mathematical logic and foundations::03B General logic
title_short Putting together Łukasiewicz and product logics
title_full Putting together Łukasiewicz and product logics
title_fullStr Putting together Łukasiewicz and product logics
title_full_unstemmed Putting together Łukasiewicz and product logics
title_sort Putting together Łukasiewicz and product logics
dc.creator.none.fl_str_mv Esteva Massaguer, Francesc
Godo Lacasa, Lluís
author Esteva Massaguer, Francesc
author_facet Esteva Massaguer, Francesc
Godo Lacasa, Lluís
author_role author
author2 Godo Lacasa, Lluís
author2_role author
dc.subject.none.fl_str_mv Ł∏ algebras
Lògica matemàtica
Classificació AMS::03 Mathematical logic and foundations::03B General logic
topic Ł∏ algebras
Lògica matemàtica
Classificació AMS::03 Mathematical logic and foundations::03B General logic
description In this paper we investigate a propositional fuzzy logical system $\L\Pi$ which contains the well-known \L ukasiewicz, Product and G\"{o}del fuzzy logics as sublogics. We define the corresponding algebraic structures, called $\L\Pi$-algebras and prove the following completeness result: a formula $\varphi$ is provable in the $\L\Pi$ logic iff it is a tautology for all linear $\L\Pi$-algebras. Moreover, linear $\L\Pi$-algebras are shown to be embeddable in linearly ordered abelian rings with a strong unit and cancellation law.
publishDate 1999
dc.date.none.fl_str_mv 1999
1999-01-01
2007
2007-09-25
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2099/3555
url https://hdl.handle.net/2099/3555
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2

http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2

http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universitat Politècnica de Catalunya. Secció de Matemàtiques i Informàtica
publisher.none.fl_str_mv Universitat Politècnica de Catalunya. Secció de Matemàtiques i Informàtica
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
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