The First-Order Hypothetical Logic of Proofs

Autores
Steren, Gabriela; Bonelli, Eduardo Augusto
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The Propositional Logic of Proofs (LP) is a modal logic in which the modality □A is revisited as [​[t]​]​A , t being an expression that bears witness to the validity of A . It enjoys arithmetical soundness and completeness, can realize all S4 theorems and is capable of reflecting its own proofs ( ⊢A implies ⊢[​[t]​]A , for some t ). A presentation of first-order LP has recently been proposed, FOLP, which enjoys arithmetical soundness and has an exact provability semantics. A key notion in this presentation is how free variables are dealt with in a formula of the form [​[t]​]​A(i) . We revisit this notion in the setting of a Natural Deduction presentation and propose a Curry–Howard correspondence for FOLP. A term assignment is provided and a proof of strong normalization is given.
Fil: Steren, Gabriela. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina
Fil: Bonelli, Eduardo Augusto. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
FIRST ORDER LOGIC OF PROOFS
CURRY HOWARD
NORMALIZATION
LAMBDA CALCULUS
Nivel de accesibilidad
acceso embargado
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:11336/42132
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling The First-Order Hypothetical Logic of ProofsSteren, GabrielaBonelli, Eduardo AugustoFIRST ORDER LOGIC OF PROOFSCURRY HOWARDNORMALIZATIONLAMBDA CALCULUShttps://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1The Propositional Logic of Proofs (LP) is a modal logic in which the modality □A is revisited as [​[t]​]​A , t being an expression that bears witness to the validity of A . It enjoys arithmetical soundness and completeness, can realize all S4 theorems and is capable of reflecting its own proofs ( ⊢A implies ⊢[​[t]​]A , for some t ). A presentation of first-order LP has recently been proposed, FOLP, which enjoys arithmetical soundness and has an exact provability semantics. A key notion in this presentation is how free variables are dealt with in a formula of the form [​[t]​]​A(i) . We revisit this notion in the setting of a Natural Deduction presentation and propose a Curry–Howard correspondence for FOLP. A term assignment is provided and a proof of strong normalization is given.Fil: Steren, Gabriela. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; ArgentinaFil: Bonelli, Eduardo Augusto. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaOxford University Press2017-09info:eu-repo/date/embargoEnd/2018-07-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/zipapplication/pdfhttp://hdl.handle.net/11336/42132Steren, Gabriela; Bonelli, Eduardo Augusto; The First-Order Hypothetical Logic of Proofs; Oxford University Press; Journal of Logic and Computation; 27; 4; 9-2017; 1023-10660955-792XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1093/logcom/exv090info:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/logcom/article-abstract/27/4/1023/2917861info:eu-repo/semantics/embargoedAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:18:55Zoai:ri.conicet.gov.ar:11336/42132instacron: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 11:18:56.245CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The First-Order Hypothetical Logic of Proofs
title The First-Order Hypothetical Logic of Proofs
spellingShingle The First-Order Hypothetical Logic of Proofs
Steren, Gabriela
FIRST ORDER LOGIC OF PROOFS
CURRY HOWARD
NORMALIZATION
LAMBDA CALCULUS
title_short The First-Order Hypothetical Logic of Proofs
title_full The First-Order Hypothetical Logic of Proofs
title_fullStr The First-Order Hypothetical Logic of Proofs
title_full_unstemmed The First-Order Hypothetical Logic of Proofs
title_sort The First-Order Hypothetical Logic of Proofs
dc.creator.none.fl_str_mv Steren, Gabriela
Bonelli, Eduardo Augusto
author Steren, Gabriela
author_facet Steren, Gabriela
Bonelli, Eduardo Augusto
author_role author
author2 Bonelli, Eduardo Augusto
author2_role author
dc.subject.none.fl_str_mv FIRST ORDER LOGIC OF PROOFS
CURRY HOWARD
NORMALIZATION
LAMBDA CALCULUS
topic FIRST ORDER LOGIC OF PROOFS
CURRY HOWARD
NORMALIZATION
LAMBDA CALCULUS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The Propositional Logic of Proofs (LP) is a modal logic in which the modality □A is revisited as [​[t]​]​A , t being an expression that bears witness to the validity of A . It enjoys arithmetical soundness and completeness, can realize all S4 theorems and is capable of reflecting its own proofs ( ⊢A implies ⊢[​[t]​]A , for some t ). A presentation of first-order LP has recently been proposed, FOLP, which enjoys arithmetical soundness and has an exact provability semantics. A key notion in this presentation is how free variables are dealt with in a formula of the form [​[t]​]​A(i) . We revisit this notion in the setting of a Natural Deduction presentation and propose a Curry–Howard correspondence for FOLP. A term assignment is provided and a proof of strong normalization is given.
Fil: Steren, Gabriela. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina
Fil: Bonelli, Eduardo Augusto. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description The Propositional Logic of Proofs (LP) is a modal logic in which the modality □A is revisited as [​[t]​]​A , t being an expression that bears witness to the validity of A . It enjoys arithmetical soundness and completeness, can realize all S4 theorems and is capable of reflecting its own proofs ( ⊢A implies ⊢[​[t]​]A , for some t ). A presentation of first-order LP has recently been proposed, FOLP, which enjoys arithmetical soundness and has an exact provability semantics. A key notion in this presentation is how free variables are dealt with in a formula of the form [​[t]​]​A(i) . We revisit this notion in the setting of a Natural Deduction presentation and propose a Curry–Howard correspondence for FOLP. A term assignment is provided and a proof of strong normalization is given.
publishDate 2017
dc.date.none.fl_str_mv 2017-09
info:eu-repo/date/embargoEnd/2018-07-01
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/11336/42132
Steren, Gabriela; Bonelli, Eduardo Augusto; The First-Order Hypothetical Logic of Proofs; Oxford University Press; Journal of Logic and Computation; 27; 4; 9-2017; 1023-1066
0955-792X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/42132
identifier_str_mv Steren, Gabriela; Bonelli, Eduardo Augusto; The First-Order Hypothetical Logic of Proofs; Oxford University Press; Journal of Logic and Computation; 27; 4; 9-2017; 1023-1066
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/exv090
info:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/logcom/article-abstract/27/4/1023/2917861
dc.rights.none.fl_str_mv info:eu-repo/semantics/embargoedAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv embargoedAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/zip
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
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score 12.982451

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