Completeness in Hybrid Type Theory

Autores
Areces, Carlos Eduardo; Blackburn, Patrick; Huertas, Antonia; Manzano, Maria
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We show that basic hybridization (adding nominals and @ operators) makes it possible to give straightforward Henkin-style completeness proofs even when the modal logic being hybridized is higher-order. The key ideas are to add nominals as expressions of type t, and to extend to arbitrary types the way we interpret @i@i in propositional and first-order hybrid logic. This means: interpret @iαa@iαa , where αaαa is an expression of any type aa , as an expression of type aa that rigidly returns the value that αaαa receives at the i-world. The axiomatization and completeness proofs are generalizations of those found in propositional and first-order hybrid logic, and (as is usual inhybrid logic) we automatically obtain a wide range of completeness results for stronger logics and languages. Our approach is deliberately low-tech. We don’t, for example, make use of Montague’s intensional type s, or Fitting-style intensional models; we build, as simply as we can, hybrid logicover Henkin’s logic.
Fil: Areces, Carlos Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Córdoba; Argentina
Fil: Blackburn, Patrick. University of Roskilde. Roskilde; Dinamarca
Fil: Huertas, Antonia. Universitat Oberta de Catalunya; España
Fil: Manzano, Maria. Universidad de Salamanca; España
Materia
Hybrid Logic
Type Theory
Higher-Order Modal Logic
Nominals
@ Operators
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:11336/33948
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Completeness in Hybrid Type TheoryAreces, Carlos EduardoBlackburn, PatrickHuertas, AntoniaManzano, MariaHybrid LogicType TheoryHigher-Order Modal LogicNominals@ Operatorshttps://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1We show that basic hybridization (adding nominals and @ operators) makes it possible to give straightforward Henkin-style completeness proofs even when the modal logic being hybridized is higher-order. The key ideas are to add nominals as expressions of type t, and to extend to arbitrary types the way we interpret @i@i in propositional and first-order hybrid logic. This means: interpret @iαa@iαa , where αaαa is an expression of any type aa , as an expression of type aa that rigidly returns the value that αaαa receives at the i-world. The axiomatization and completeness proofs are generalizations of those found in propositional and first-order hybrid logic, and (as is usual inhybrid logic) we automatically obtain a wide range of completeness results for stronger logics and languages. Our approach is deliberately low-tech. We don’t, for example, make use of Montague’s intensional type s, or Fitting-style intensional models; we build, as simply as we can, hybrid logicover Henkin’s logic.Fil: Areces, Carlos Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Córdoba; ArgentinaFil: Blackburn, Patrick. University of Roskilde. Roskilde; DinamarcaFil: Huertas, Antonia. Universitat Oberta de Catalunya; EspañaFil: Manzano, Maria. Universidad de Salamanca; EspañaSpringer2014-05info: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/11336/33948Areces, Carlos Eduardo; Blackburn, Patrick; Huertas, Antonia; Manzano, Maria; Completeness in Hybrid Type Theory; Springer; Journal of Philosophical Logic; 43; 2-3; 5-2014; 209-2380022-3611CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s10992-012-9260-4info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs10992-012-9260-4info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:27:53Zoai:ri.conicet.gov.ar:11336/33948instacron: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:34982025-10-22 11:27:54.289CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Completeness in Hybrid Type Theory
title Completeness in Hybrid Type Theory
spellingShingle Completeness in Hybrid Type Theory
Areces, Carlos Eduardo
Hybrid Logic
Type Theory
Higher-Order Modal Logic
Nominals
@ Operators
title_short Completeness in Hybrid Type Theory
title_full Completeness in Hybrid Type Theory
title_fullStr Completeness in Hybrid Type Theory
title_full_unstemmed Completeness in Hybrid Type Theory
title_sort Completeness in Hybrid Type Theory
dc.creator.none.fl_str_mv Areces, Carlos Eduardo
Blackburn, Patrick
Huertas, Antonia
Manzano, Maria
author Areces, Carlos Eduardo
author_facet Areces, Carlos Eduardo
Blackburn, Patrick
Huertas, Antonia
Manzano, Maria
author_role author
author2 Blackburn, Patrick
Huertas, Antonia
Manzano, Maria
author2_role author
author
author
dc.subject.none.fl_str_mv Hybrid Logic
Type Theory
Higher-Order Modal Logic
Nominals
@ Operators
topic Hybrid Logic
Type Theory
Higher-Order Modal Logic
Nominals
@ Operators
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We show that basic hybridization (adding nominals and @ operators) makes it possible to give straightforward Henkin-style completeness proofs even when the modal logic being hybridized is higher-order. The key ideas are to add nominals as expressions of type t, and to extend to arbitrary types the way we interpret @i@i in propositional and first-order hybrid logic. This means: interpret @iαa@iαa , where αaαa is an expression of any type aa , as an expression of type aa that rigidly returns the value that αaαa receives at the i-world. The axiomatization and completeness proofs are generalizations of those found in propositional and first-order hybrid logic, and (as is usual inhybrid logic) we automatically obtain a wide range of completeness results for stronger logics and languages. Our approach is deliberately low-tech. We don’t, for example, make use of Montague’s intensional type s, or Fitting-style intensional models; we build, as simply as we can, hybrid logicover Henkin’s logic.
Fil: Areces, Carlos Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Córdoba; Argentina
Fil: Blackburn, Patrick. University of Roskilde. Roskilde; Dinamarca
Fil: Huertas, Antonia. Universitat Oberta de Catalunya; España
Fil: Manzano, Maria. Universidad de Salamanca; España
description We show that basic hybridization (adding nominals and @ operators) makes it possible to give straightforward Henkin-style completeness proofs even when the modal logic being hybridized is higher-order. The key ideas are to add nominals as expressions of type t, and to extend to arbitrary types the way we interpret @i@i in propositional and first-order hybrid logic. This means: interpret @iαa@iαa , where αaαa is an expression of any type aa , as an expression of type aa that rigidly returns the value that αaαa receives at the i-world. The axiomatization and completeness proofs are generalizations of those found in propositional and first-order hybrid logic, and (as is usual inhybrid logic) we automatically obtain a wide range of completeness results for stronger logics and languages. Our approach is deliberately low-tech. We don’t, for example, make use of Montague’s intensional type s, or Fitting-style intensional models; we build, as simply as we can, hybrid logicover Henkin’s logic.
publishDate 2014
dc.date.none.fl_str_mv 2014-05
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/11336/33948
Areces, Carlos Eduardo; Blackburn, Patrick; Huertas, Antonia; Manzano, Maria; Completeness in Hybrid Type Theory; Springer; Journal of Philosophical Logic; 43; 2-3; 5-2014; 209-238
0022-3611
CONICET Digital
CONICET
url http://hdl.handle.net/11336/33948
identifier_str_mv Areces, Carlos Eduardo; Blackburn, Patrick; Huertas, Antonia; Manzano, Maria; Completeness in Hybrid Type Theory; Springer; Journal of Philosophical Logic; 43; 2-3; 5-2014; 209-238
0022-3611
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s10992-012-9260-4
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs10992-012-9260-4
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 12.982451

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