On some semi-intuitionistic logics
- Autores
- Cornejo, Juan Manuel; Viglizzo, Ignacio Dario
- Año de publicación
- 2015
- Idioma
- español castellano
- Tipo de recurso
- documento de conferencia
- Estado
- versión publicada
- Descripción
- Semi-intuitionistic logic is the logic counterpart to semi-Heyting algebras, which weredefined by H. P. Sankappanavar in [3] as a variety generalizing the one of Heyting algebraswhile retaining some important features, like the fact that they are all pseudocomplementeddistributive lattices and their congruences are determined by filters. Semi-Heyting algebrasare algebras A = hA,∨,∧,→,>,⊥i that satisfy the conditions:(SH1) hA,∨,∧,>,⊥i is a bounded lattice(SH2) x∧(x → y) ≈ x∧y(SH3) x∧(y → z) ≈ x∧[(x∧y) → (x∧z)](SH4) x → x ≈ >.We present a new, more streamlined set of axioms for semi-intuitionistic logic, which weprove translationally equivalent to the one introduced in [1]. We then study some formulasthat define a semi-Heyting implication, and specialize this study to the case in which theformulas use only the lattice operators and the intuitionistic implication. We prove thenthat all the logics thus obtained are equivalent to intuitionistic logic, and give their Kripkesemantics.This work has been published in Studia Logica [2].
Fil: Cornejo, Juan Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
Fil: Viglizzo, Ignacio Dario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
XIII Congreso Dr. Antonio Monteiro
Bahia Blanca
Argentina
Universidad Nacional del Sur. Departamento de Matemática
Instituto de Matemática de Bahía Blanca - Materia
-
LOGICA SEMI INTUICIONISTA
HEYTING
SEMI HEYTING - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
.jpg)
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/155487
Ver los metadatos del registro completo
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On some semi-intuitionistic logicsCornejo, Juan ManuelViglizzo, Ignacio DarioLOGICA SEMI INTUICIONISTAHEYTINGSEMI HEYTINGhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Semi-intuitionistic logic is the logic counterpart to semi-Heyting algebras, which weredefined by H. P. Sankappanavar in [3] as a variety generalizing the one of Heyting algebraswhile retaining some important features, like the fact that they are all pseudocomplementeddistributive lattices and their congruences are determined by filters. Semi-Heyting algebrasare algebras A = hA,∨,∧,→,>,⊥i that satisfy the conditions:(SH1) hA,∨,∧,>,⊥i is a bounded lattice(SH2) x∧(x → y) ≈ x∧y(SH3) x∧(y → z) ≈ x∧[(x∧y) → (x∧z)](SH4) x → x ≈ >.We present a new, more streamlined set of axioms for semi-intuitionistic logic, which weprove translationally equivalent to the one introduced in [1]. We then study some formulasthat define a semi-Heyting implication, and specialize this study to the case in which theformulas use only the lattice operators and the intuitionistic implication. We prove thenthat all the logics thus obtained are equivalent to intuitionistic logic, and give their Kripkesemantics.This work has been published in Studia Logica [2].Fil: Cornejo, Juan Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: Viglizzo, Ignacio Dario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaXIII Congreso Dr. Antonio MonteiroBahia BlancaArgentinaUniversidad Nacional del Sur. Departamento de MatemáticaInstituto de Matemática de Bahía BlancaInstituto de Matemática de Bahía Blanca2015info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/conferenceObjectCongresoJournalhttp://purl.org/coar/resource_type/c_5794info:ar-repo/semantics/documentoDeConferenciaapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/155487On some semi-intuitionistic logics; XIII Congreso Dr. Antonio Monteiro; Bahia Blanca; Argentina; 2015; 1430327-9170CONICET DigitalCONICETspainfo:eu-repo/semantics/altIdentifier/url/http://inmabb.conicet.gob.ar/publicaciones/actas-del-congreso-monteiro/13Internacionalinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:07:53Zoai:ri.conicet.gov.ar:11336/155487instacron: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 10:07:53.556CONICET 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 LOGICA SEMI INTUICIONISTA HEYTING SEMI HEYTING |
| 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 |
LOGICA SEMI INTUICIONISTA HEYTING SEMI HEYTING |
| topic |
LOGICA SEMI INTUICIONISTA HEYTING SEMI HEYTING |
| 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 weredefined by H. P. Sankappanavar in [3] as a variety generalizing the one of Heyting algebraswhile retaining some important features, like the fact that they are all pseudocomplementeddistributive lattices and their congruences are determined by filters. Semi-Heyting algebrasare algebras A = hA,∨,∧,→,>,⊥i that satisfy the conditions:(SH1) hA,∨,∧,>,⊥i is a bounded lattice(SH2) x∧(x → y) ≈ x∧y(SH3) x∧(y → z) ≈ x∧[(x∧y) → (x∧z)](SH4) x → x ≈ >.We present a new, more streamlined set of axioms for semi-intuitionistic logic, which weprove translationally equivalent to the one introduced in [1]. We then study some formulasthat define a semi-Heyting implication, and specialize this study to the case in which theformulas use only the lattice operators and the intuitionistic implication. We prove thenthat all the logics thus obtained are equivalent to intuitionistic logic, and give their Kripkesemantics.This work has been published in Studia Logica [2]. Fil: Cornejo, Juan Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina Fil: Viglizzo, Ignacio Dario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina XIII Congreso Dr. Antonio Monteiro Bahia Blanca Argentina Universidad Nacional del Sur. Departamento de Matemática Instituto de Matemática de Bahía Blanca |
| description |
Semi-intuitionistic logic is the logic counterpart to semi-Heyting algebras, which weredefined by H. P. Sankappanavar in [3] as a variety generalizing the one of Heyting algebraswhile retaining some important features, like the fact that they are all pseudocomplementeddistributive lattices and their congruences are determined by filters. Semi-Heyting algebrasare algebras A = hA,∨,∧,→,>,⊥i that satisfy the conditions:(SH1) hA,∨,∧,>,⊥i is a bounded lattice(SH2) x∧(x → y) ≈ x∧y(SH3) x∧(y → z) ≈ x∧[(x∧y) → (x∧z)](SH4) x → x ≈ >.We present a new, more streamlined set of axioms for semi-intuitionistic logic, which weprove translationally equivalent to the one introduced in [1]. We then study some formulasthat define a semi-Heyting implication, and specialize this study to the case in which theformulas use only the lattice operators and the intuitionistic implication. We prove thenthat all the logics thus obtained are equivalent to intuitionistic logic, and give their Kripkesemantics.This work has been published in Studia Logica [2]. |
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2015 |
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2015 |
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