A semantics for equational hybrid propositional type theory

The definition of identity in terms of other logical symbols is a recurrent issue in logic. In particular, in First-Order Logic (FOL) there is no way of defining the global relation of identity, while in standard Second-Order Logic (SOL) this definition is not only possible, but widely used. In this...

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Detalles Bibliográficos
Autores: Manzano Arjona, María, Martins, Manuel A., Huertas, M. Antonia
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2014
País:España
Institución:Universitat Oberta de Catalunya (UOC)
Repositorio:O2, repositorio institucional de la UOC
OAI Identifier:oai:openaccess.uoc.edu:10609/123586
Acceso en línea:https://hdl.handle.net/10609/123586
Access Level:acceso abierto
Palabra clave:propositional type theory
first-order logic
second-order logic
equational hybrid logic
lógica de primer orden
lógica de segundo orden
teoría de tipo proposicional
lógica ecuacional híbrida
lògica de primer ordre
lògica de segon ordre
teoria de tipus proposicional
lògica equacional híbrida
Logic, Modern
Lògica moderna
Lógica moderna
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spelling A semantics for equational hybrid propositional type theoryManzano Arjona, MaríaMartins, Manuel A.Huertas, M. Antoniapropositional type theoryfirst-order logicsecond-order logicequational hybrid logiclógica de primer ordenlógica de segundo ordenteoría de tipo proposicionallógica ecuacional híbridalògica de primer ordrelògica de segon ordreteoria de tipus proposicionallògica equacional híbridaLogic, ModernLògica modernaLógica modernaThe definition of identity in terms of other logical symbols is a recurrent issue in logic. In particular, in First-Order Logic (FOL) there is no way of defining the global relation of identity, while in standard Second-Order Logic (SOL) this definition is not only possible, but widely used. In this paper, the reverse question is posed and affirmatively answered: Can we define with only equality and abstraction the remaining logical symbols? Our present work is developed in the context of an equational hybrid logic (i.e. a modal logic with equations as propositional atoms enlarged with the hybrid expressions: nominals and the @ operator). Our logical base is propositional type theory. We take the propositional equality, abstraction, nominals, and @ operators as primitive symbols and we demonstrate that all of the remaining logical symbols can be defined, including propositional quantifiers and equational equality.Bulletin of the Section of LogicUniversidade de AveiroUniversidad de SalamancaUniversitat Oberta de Catalunya (UOC)202020202014info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/10609/123586reponame:O2, repositorio institucional de la UOCinstname:Universitat Oberta de Catalunya (UOC)InglésBulletin of the Section of Logic, 2014, 43(3-4)http://www.filozof.uni.lodz.pl/bulletin/pdf/43_34_1.pdfinfo:eu-repo/grantAgreement/FFI-2009-09345MICINN//info:eu-repo/grantAgreement/FFI2013-47126-P//info:eu-repo/grantAgreement/FP7-PEOPLE-2012-IRSES//info:eu-repo/grantAgreement/FCOMP-01-0124-FEDER-028923//info:eu-repo/grantAgreement/PEst-OE/MAT/UI4106CC BY-NC-NDhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:openaccess.uoc.edu:10609/1235862026-05-28T12:42:01Z
dc.title.none.fl_str_mv A semantics for equational hybrid propositional type theory
title A semantics for equational hybrid propositional type theory
spellingShingle A semantics for equational hybrid propositional type theory
Manzano Arjona, María
propositional type theory
first-order logic
second-order logic
equational hybrid logic
lógica de primer orden
lógica de segundo orden
teoría de tipo proposicional
lógica ecuacional híbrida
lògica de primer ordre
lògica de segon ordre
teoria de tipus proposicional
lògica equacional híbrida
Logic, Modern
Lògica moderna
Lógica moderna
title_short A semantics for equational hybrid propositional type theory
title_full A semantics for equational hybrid propositional type theory
title_fullStr A semantics for equational hybrid propositional type theory
title_full_unstemmed A semantics for equational hybrid propositional type theory
title_sort A semantics for equational hybrid propositional type theory
dc.creator.none.fl_str_mv Manzano Arjona, María
Martins, Manuel A.
Huertas, M. Antonia
author Manzano Arjona, María
author_facet Manzano Arjona, María
Martins, Manuel A.
Huertas, M. Antonia
author_role author
author2 Martins, Manuel A.
Huertas, M. Antonia
author2_role author
author
dc.contributor.none.fl_str_mv Universidade de Aveiro
Universidad de Salamanca
Universitat Oberta de Catalunya (UOC)
dc.subject.none.fl_str_mv propositional type theory
first-order logic
second-order logic
equational hybrid logic
lógica de primer orden
lógica de segundo orden
teoría de tipo proposicional
lógica ecuacional híbrida
lògica de primer ordre
lògica de segon ordre
teoria de tipus proposicional
lògica equacional híbrida
Logic, Modern
Lògica moderna
Lógica moderna
topic propositional type theory
first-order logic
second-order logic
equational hybrid logic
lógica de primer orden
lógica de segundo orden
teoría de tipo proposicional
lógica ecuacional híbrida
lògica de primer ordre
lògica de segon ordre
teoria de tipus proposicional
lògica equacional híbrida
Logic, Modern
Lògica moderna
Lógica moderna
description The definition of identity in terms of other logical symbols is a recurrent issue in logic. In particular, in First-Order Logic (FOL) there is no way of defining the global relation of identity, while in standard Second-Order Logic (SOL) this definition is not only possible, but widely used. In this paper, the reverse question is posed and affirmatively answered: Can we define with only equality and abstraction the remaining logical symbols? Our present work is developed in the context of an equational hybrid logic (i.e. a modal logic with equations as propositional atoms enlarged with the hybrid expressions: nominals and the @ operator). Our logical base is propositional type theory. We take the propositional equality, abstraction, nominals, and @ operators as primitive symbols and we demonstrate that all of the remaining logical symbols can be defined, including propositional quantifiers and equational equality.
publishDate 2014
dc.date.none.fl_str_mv 2014
2020
2020
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/10609/123586
url https://hdl.handle.net/10609/123586
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Bulletin of the Section of Logic, 2014, 43(3-4)
http://www.filozof.uni.lodz.pl/bulletin/pdf/43_34_1.pdf
info:eu-repo/grantAgreement/FFI-2009-09345MICINN//
info:eu-repo/grantAgreement/FFI2013-47126-P//
info:eu-repo/grantAgreement/FP7-PEOPLE-2012-IRSES//
info:eu-repo/grantAgreement/FCOMP-01-0124-FEDER-028923//
info:eu-repo/grantAgreement/PEst-OE/MAT/UI4106
dc.rights.none.fl_str_mv CC BY-NC-ND
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv CC BY-NC-ND
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Bulletin of the Section of Logic
publisher.none.fl_str_mv Bulletin of the Section of Logic
dc.source.none.fl_str_mv reponame:O2, repositorio institucional de la UOC
instname:Universitat Oberta de Catalunya (UOC)
instname_str Universitat Oberta de Catalunya (UOC)
reponame_str O2, repositorio institucional de la UOC
collection O2, repositorio institucional de la UOC
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869423124126105600
score 15.301603

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