Constructive logic with strong negation as a substructural logic

Autores
Busaniche, Manuela; Cignoli, Roberto Leonardo Oscar
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Spinks and Veroff have shown that constructive logic with strong negation (CLSN for short), can be considered as a substructural logic. We use algebraic tools developed to study substructural logics to investigate some axiomatic extensions of CLSN. For instance, we prove that Nilpotent minimum logic is the extension of CLSN by the prelinearity axiom. This generalizes the well-known result by Monteiro and Vakarelov that three-valued ukasiewicz logic is an extension of CLSN. A Glivenko-like theorem relating CLSN and three-valued ukasiewicz logic is proved.
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: Cignoli, Roberto Leonardo Oscar. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Materia
Constructive Logic
Heyting Algebras
Nelson Algebras
Nilpotent Minimum Logic
Residuated Lattices
Strong Negation
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:11336/75191
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/75191
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Constructive logic with strong negation as a substructural logicBusaniche, ManuelaCignoli, Roberto Leonardo OscarConstructive LogicHeyting AlgebrasNelson AlgebrasNilpotent Minimum LogicResiduated LatticesStrong Negationhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Spinks and Veroff have shown that constructive logic with strong negation (CLSN for short), can be considered as a substructural logic. We use algebraic tools developed to study substructural logics to investigate some axiomatic extensions of CLSN. For instance, we prove that Nilpotent minimum logic is the extension of CLSN by the prelinearity axiom. This generalizes the well-known result by Monteiro and Vakarelov that three-valued ukasiewicz logic is an extension of CLSN. A Glivenko-like theorem relating CLSN and three-valued ukasiewicz logic is proved.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: Cignoli, Roberto Leonardo Oscar. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaOxford University Press2010-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/75191Busaniche, Manuela; Cignoli, Roberto Leonardo Oscar; Constructive logic with strong negation as a substructural logic; Oxford University Press; Journal of Logic and Computation; 20; 4; 8-2010; 761-7930955-792XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1093/logcom/exn081info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-05T10:30:46Zoai:ri.conicet.gov.ar:11336/75191instacron: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:34982025-11-05 10:30:47.179CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Constructive logic with strong negation as a substructural logic
title Constructive logic with strong negation as a substructural logic
spellingShingle Constructive logic with strong negation as a substructural logic
Busaniche, Manuela
Constructive Logic
Heyting Algebras
Nelson Algebras
Nilpotent Minimum Logic
Residuated Lattices
Strong Negation
title_short Constructive logic with strong negation as a substructural logic
title_full Constructive logic with strong negation as a substructural logic
title_fullStr Constructive logic with strong negation as a substructural logic
title_full_unstemmed Constructive logic with strong negation as a substructural logic
title_sort Constructive logic with strong negation as a substructural logic
dc.creator.none.fl_str_mv Busaniche, Manuela
Cignoli, Roberto Leonardo Oscar
author Busaniche, Manuela
author_facet Busaniche, Manuela
Cignoli, Roberto Leonardo Oscar
author_role author
author2 Cignoli, Roberto Leonardo Oscar
author2_role author
dc.subject.none.fl_str_mv Constructive Logic
Heyting Algebras
Nelson Algebras
Nilpotent Minimum Logic
Residuated Lattices
Strong Negation
topic Constructive Logic
Heyting Algebras
Nelson Algebras
Nilpotent Minimum Logic
Residuated Lattices
Strong Negation
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Spinks and Veroff have shown that constructive logic with strong negation (CLSN for short), can be considered as a substructural logic. We use algebraic tools developed to study substructural logics to investigate some axiomatic extensions of CLSN. For instance, we prove that Nilpotent minimum logic is the extension of CLSN by the prelinearity axiom. This generalizes the well-known result by Monteiro and Vakarelov that three-valued ukasiewicz logic is an extension of CLSN. A Glivenko-like theorem relating CLSN and three-valued ukasiewicz logic is proved.
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: Cignoli, Roberto Leonardo Oscar. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
description Spinks and Veroff have shown that constructive logic with strong negation (CLSN for short), can be considered as a substructural logic. We use algebraic tools developed to study substructural logics to investigate some axiomatic extensions of CLSN. For instance, we prove that Nilpotent minimum logic is the extension of CLSN by the prelinearity axiom. This generalizes the well-known result by Monteiro and Vakarelov that three-valued ukasiewicz logic is an extension of CLSN. A Glivenko-like theorem relating CLSN and three-valued ukasiewicz logic is proved.
publishDate 2010
dc.date.none.fl_str_mv 2010-08
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/11336/75191
Busaniche, Manuela; Cignoli, Roberto Leonardo Oscar; Constructive logic with strong negation as a substructural logic; Oxford University Press; Journal of Logic and Computation; 20; 4; 8-2010; 761-793
0955-792X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/75191
identifier_str_mv Busaniche, Manuela; Cignoli, Roberto Leonardo Oscar; Constructive logic with strong negation as a substructural logic; Oxford University Press; Journal of Logic and Computation; 20; 4; 8-2010; 761-793
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/exn081
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
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
_version_ 1847977978650165248
score 13.087074

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