On structural completeness versus almost structural completeness problem: A discriminator varieties case study

Autores
Campercholi, Miguel Alejandro Carlos; Stronkowski, Michal; Vaggione, Diego Jose
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the following problem: determine which almost structurally complete quasivarieties are structurally complete. We propose a general solution to this problem and then a solution in the semisimple case. As a consequence, we obtain a characterization of structurally complete discriminator varieties. An interesting corollary in logic follows: Let L be a propositional logic/deductive system in the language with formulas for verum, which is a theorem, and falsum, which is not a theorem. Assume also that L has an adequate semantics given by a discriminator variety. Then L is structurally complete if and only if it is maximal. All such logics/deductive systems are almost structurally complete.
Fil: Campercholi, Miguel Alejandro Carlos. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Fil: Stronkowski, Michal. Warsaw University of Technology; Polonia
Fil: Vaggione, Diego Jose. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Materia
Structural Completeness
Almost Structural Completeness
Minimal Varieties
Minimal Quasivarieties
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:11336/32195
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/32195
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling On structural completeness versus almost structural completeness problem: A discriminator varieties case studyCampercholi, Miguel Alejandro CarlosStronkowski, MichalVaggione, Diego JoseStructural CompletenessAlmost Structural CompletenessMinimal VarietiesMinimal Quasivarietieshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the following problem: determine which almost structurally complete quasivarieties are structurally complete. We propose a general solution to this problem and then a solution in the semisimple case. As a consequence, we obtain a characterization of structurally complete discriminator varieties. An interesting corollary in logic follows: Let L be a propositional logic/deductive system in the language with formulas for verum, which is a theorem, and falsum, which is not a theorem. Assume also that L has an adequate semantics given by a discriminator variety. Then L is structurally complete if and only if it is maximal. All such logics/deductive systems are almost structurally complete.Fil: Campercholi, Miguel Alejandro Carlos. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Stronkowski, Michal. Warsaw University of Technology; PoloniaFil: Vaggione, Diego Jose. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaOxford University Press2014-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/32195Campercholi, Miguel Alejandro Carlos; Vaggione, Diego Jose; Stronkowski, Michal; On structural completeness versus almost structural completeness problem: A discriminator varieties case study; Oxford University Press; Logic Journal Of The Igpl (print); 23; 2; 12-2014; 235-2461367-0751CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1093/jigpal/jzu032info:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/jigpal/article-abstract/23/2/235/651382?redirectedFrom=fulltextinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:09:39Zoai:ri.conicet.gov.ar:11336/32195instacron: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:34982025-10-15 15:09:39.896CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On structural completeness versus almost structural completeness problem: A discriminator varieties case study
title On structural completeness versus almost structural completeness problem: A discriminator varieties case study
spellingShingle On structural completeness versus almost structural completeness problem: A discriminator varieties case study
Campercholi, Miguel Alejandro Carlos
Structural Completeness
Almost Structural Completeness
Minimal Varieties
Minimal Quasivarieties
title_short On structural completeness versus almost structural completeness problem: A discriminator varieties case study
title_full On structural completeness versus almost structural completeness problem: A discriminator varieties case study
title_fullStr On structural completeness versus almost structural completeness problem: A discriminator varieties case study
title_full_unstemmed On structural completeness versus almost structural completeness problem: A discriminator varieties case study
title_sort On structural completeness versus almost structural completeness problem: A discriminator varieties case study
dc.creator.none.fl_str_mv Campercholi, Miguel Alejandro Carlos
Stronkowski, Michal
Vaggione, Diego Jose
author Campercholi, Miguel Alejandro Carlos
author_facet Campercholi, Miguel Alejandro Carlos
Stronkowski, Michal
Vaggione, Diego Jose
author_role author
author2 Stronkowski, Michal
Vaggione, Diego Jose
author2_role author
author
dc.subject.none.fl_str_mv Structural Completeness
Almost Structural Completeness
Minimal Varieties
Minimal Quasivarieties
topic Structural Completeness
Almost Structural Completeness
Minimal Varieties
Minimal Quasivarieties
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 study the following problem: determine which almost structurally complete quasivarieties are structurally complete. We propose a general solution to this problem and then a solution in the semisimple case. As a consequence, we obtain a characterization of structurally complete discriminator varieties. An interesting corollary in logic follows: Let L be a propositional logic/deductive system in the language with formulas for verum, which is a theorem, and falsum, which is not a theorem. Assume also that L has an adequate semantics given by a discriminator variety. Then L is structurally complete if and only if it is maximal. All such logics/deductive systems are almost structurally complete.
Fil: Campercholi, Miguel Alejandro Carlos. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Fil: Stronkowski, Michal. Warsaw University of Technology; Polonia
Fil: Vaggione, Diego Jose. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
description We study the following problem: determine which almost structurally complete quasivarieties are structurally complete. We propose a general solution to this problem and then a solution in the semisimple case. As a consequence, we obtain a characterization of structurally complete discriminator varieties. An interesting corollary in logic follows: Let L be a propositional logic/deductive system in the language with formulas for verum, which is a theorem, and falsum, which is not a theorem. Assume also that L has an adequate semantics given by a discriminator variety. Then L is structurally complete if and only if it is maximal. All such logics/deductive systems are almost structurally complete.
publishDate 2014
dc.date.none.fl_str_mv 2014-12
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/11336/32195
Campercholi, Miguel Alejandro Carlos; Vaggione, Diego Jose; Stronkowski, Michal; On structural completeness versus almost structural completeness problem: A discriminator varieties case study; Oxford University Press; Logic Journal Of The Igpl (print); 23; 2; 12-2014; 235-246
1367-0751
CONICET Digital
CONICET
url http://hdl.handle.net/11336/32195
identifier_str_mv Campercholi, Miguel Alejandro Carlos; Vaggione, Diego Jose; Stronkowski, Michal; On structural completeness versus almost structural completeness problem: A discriminator varieties case study; Oxford University Press; Logic Journal Of The Igpl (print); 23; 2; 12-2014; 235-246
1367-0751
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/jigpal/jzu032
info:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/jigpal/article-abstract/23/2/235/651382?redirectedFrom=fulltext
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 12.891075

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