On Some Semi-Intuitionistic Logics

Autores
Cornejo, Juan Manuel; Viglizzo, Ignacio Dario
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Semi-intuitionistic logic is the logic counterpart to semi-Heyting algebras, which were defined by H. P. Sankappanavar as a generalization of Heyting algebras. We present a new, more streamlined set of axioms for semi-intuitionistic logic, which we prove translationally equivalent to the original one. We then study some formulas that define a semi-Heyting implication, and specialize this study to the case in which the formulas use only the lattice operators and the intuitionistic implication. We prove then that all the logics thus obtained are equivalent to intuitionistic logic, and give their Kripke semantics.
Fil: Cornejo, Juan Manuel. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina
Fil: Viglizzo, Ignacio Dario. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina
Materia
Heyting Algebras
Intuitionistic Logic
Semi-Heyting Algebras
Semi-Intuitionistic Logic
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:11336/77848
Acceder
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network_name_str CONICET Digital (CONICET)
spelling On Some Semi-Intuitionistic LogicsCornejo, Juan ManuelViglizzo, Ignacio DarioHeyting AlgebrasIntuitionistic LogicSemi-Heyting AlgebrasSemi-Intuitionistic Logichttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Semi-intuitionistic logic is the logic counterpart to semi-Heyting algebras, which were defined by H. P. Sankappanavar as a generalization of Heyting algebras. We present a new, more streamlined set of axioms for semi-intuitionistic logic, which we prove translationally equivalent to the original one. We then study some formulas that define a semi-Heyting implication, and specialize this study to the case in which the formulas use only the lattice operators and the intuitionistic implication. We prove then that all the logics thus obtained are equivalent to intuitionistic logic, and give their Kripke semantics.Fil: Cornejo, Juan Manuel. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; ArgentinaFil: Viglizzo, Ignacio Dario. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; ArgentinaSpringer2015-04-05info: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/11336/77848Cornejo, Juan Manuel; Viglizzo, Ignacio Dario; On Some Semi-Intuitionistic Logics; Springer; Studia Logica; 103; 2; 5-4-2015; 303-3440039-32151572-8730CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s11225-014-9568-xinfo:eu-repo/semantics/altIdentifier/doi/10.1007/s11225-014-9568-xinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:06:23Zoai:ri.conicet.gov.ar:11336/77848instacron: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:34982025-09-03 10:06:23.8CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On Some Semi-Intuitionistic Logics
title On Some Semi-Intuitionistic Logics
spellingShingle On Some Semi-Intuitionistic Logics
Cornejo, Juan Manuel
Heyting Algebras
Intuitionistic Logic
Semi-Heyting Algebras
Semi-Intuitionistic Logic
title_short On Some Semi-Intuitionistic Logics
title_full On Some Semi-Intuitionistic Logics
title_fullStr On Some Semi-Intuitionistic Logics
title_full_unstemmed On Some Semi-Intuitionistic Logics
title_sort On Some Semi-Intuitionistic Logics
dc.creator.none.fl_str_mv Cornejo, Juan Manuel
Viglizzo, Ignacio Dario
author Cornejo, Juan Manuel
author_facet Cornejo, Juan Manuel
Viglizzo, Ignacio Dario
author_role author
author2 Viglizzo, Ignacio Dario
author2_role author
dc.subject.none.fl_str_mv Heyting Algebras
Intuitionistic Logic
Semi-Heyting Algebras
Semi-Intuitionistic Logic
topic Heyting Algebras
Intuitionistic Logic
Semi-Heyting Algebras
Semi-Intuitionistic Logic
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Semi-intuitionistic logic is the logic counterpart to semi-Heyting algebras, which were defined by H. P. Sankappanavar as a generalization of Heyting algebras. We present a new, more streamlined set of axioms for semi-intuitionistic logic, which we prove translationally equivalent to the original one. We then study some formulas that define a semi-Heyting implication, and specialize this study to the case in which the formulas use only the lattice operators and the intuitionistic implication. We prove then that all the logics thus obtained are equivalent to intuitionistic logic, and give their Kripke semantics.
Fil: Cornejo, Juan Manuel. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina
Fil: Viglizzo, Ignacio Dario. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina
description Semi-intuitionistic logic is the logic counterpart to semi-Heyting algebras, which were defined by H. P. Sankappanavar as a generalization of Heyting algebras. We present a new, more streamlined set of axioms for semi-intuitionistic logic, which we prove translationally equivalent to the original one. We then study some formulas that define a semi-Heyting implication, and specialize this study to the case in which the formulas use only the lattice operators and the intuitionistic implication. We prove then that all the logics thus obtained are equivalent to intuitionistic logic, and give their Kripke semantics.
publishDate 2015
dc.date.none.fl_str_mv 2015-04-05
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/11336/77848
Cornejo, Juan Manuel; Viglizzo, Ignacio Dario; On Some Semi-Intuitionistic Logics; Springer; Studia Logica; 103; 2; 5-4-2015; 303-344
0039-3215
1572-8730
CONICET Digital
CONICET
url http://hdl.handle.net/11336/77848
identifier_str_mv Cornejo, Juan Manuel; Viglizzo, Ignacio Dario; On Some Semi-Intuitionistic Logics; Springer; Studia Logica; 103; 2; 5-4-2015; 303-344
0039-3215
1572-8730
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s11225-014-9568-x
info:eu-repo/semantics/altIdentifier/doi/10.1007/s11225-014-9568-x
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 Springer
publisher.none.fl_str_mv Springer
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 13.13397

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