η-conversions of IPC implemented in atomic F

Detalhes bibliográficos
Autor(a) principal: Ferreira, Gilda
Data de Publicação: 2017
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.2/7091
Resumo: It is known that the β-conversions of the full intuitionistic propositional calculus (IPC) translate into βη-conversions of the atomic polymorphic calculus Fat. Since Fat enjoys the property of strong normalization for βη-conversions, an alternative proof of strong normalization for IPC considering β-conversions can be derived. In the present article, we improve the previous result by analysing the translation of the η-conversions of the latter calculus into a technical variant of the former system (the atomic polymorphic calculus Fat^∧_at). In fact, from the strong normalization of Fat^∧_at we can derive the strong normalization of the full intuitionistic propositional calculus considering all the standard (β and η) conversions.
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spelling η-conversions of IPC implemented in atomic FMathematical logicEta-conversionsPredicative polymorphismIntuitionistic propositional calculusStrong normalizationNatural deductionIt is known that the β-conversions of the full intuitionistic propositional calculus (IPC) translate into βη-conversions of the atomic polymorphic calculus Fat. Since Fat enjoys the property of strong normalization for βη-conversions, an alternative proof of strong normalization for IPC considering β-conversions can be derived. In the present article, we improve the previous result by analysing the translation of the η-conversions of the latter calculus into a technical variant of the former system (the atomic polymorphic calculus Fat^∧_at). In fact, from the strong normalization of Fat^∧_at we can derive the strong normalization of the full intuitionistic propositional calculus considering all the standard (β and η) conversions.Oxford University PressRepositório AbertoFerreira, Gilda2018-05-31T00:30:12Z20172017-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/7091engGilda Ferreira - η-conversions of IPC implemented in atomic F. "Logic Journal of the IGPL" [Em linha]. ISSN 1367-0751 (Print) 1368-9894 (Online). Vol. 25, nº 2 (2017), p. 115–1301367-0751 (Print)10.1093/jigpal/jzw035info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-11-16T15:26:00Zoai:repositorioaberto.uab.pt:10400.2/7091Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:47:27.289662Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv η-conversions of IPC implemented in atomic F
title η-conversions of IPC implemented in atomic F
spellingShingle η-conversions of IPC implemented in atomic F
Ferreira, Gilda
Mathematical logic
Eta-conversions
Predicative polymorphism
Intuitionistic propositional calculus
Strong normalization
Natural deduction
title_short η-conversions of IPC implemented in atomic F
title_full η-conversions of IPC implemented in atomic F
title_fullStr η-conversions of IPC implemented in atomic F
title_full_unstemmed η-conversions of IPC implemented in atomic F
title_sort η-conversions of IPC implemented in atomic F
author Ferreira, Gilda
author_facet Ferreira, Gilda
author_role author
dc.contributor.none.fl_str_mv Repositório Aberto
dc.contributor.author.fl_str_mv Ferreira, Gilda
dc.subject.por.fl_str_mv Mathematical logic
Eta-conversions
Predicative polymorphism
Intuitionistic propositional calculus
Strong normalization
Natural deduction
topic Mathematical logic
Eta-conversions
Predicative polymorphism
Intuitionistic propositional calculus
Strong normalization
Natural deduction
description It is known that the β-conversions of the full intuitionistic propositional calculus (IPC) translate into βη-conversions of the atomic polymorphic calculus Fat. Since Fat enjoys the property of strong normalization for βη-conversions, an alternative proof of strong normalization for IPC considering β-conversions can be derived. In the present article, we improve the previous result by analysing the translation of the η-conversions of the latter calculus into a technical variant of the former system (the atomic polymorphic calculus Fat^∧_at). In fact, from the strong normalization of Fat^∧_at we can derive the strong normalization of the full intuitionistic propositional calculus considering all the standard (β and η) conversions.
publishDate 2017
dc.date.none.fl_str_mv 2017
2017-01-01T00:00:00Z
2018-05-31T00:30:12Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.2/7091
url http://hdl.handle.net/10400.2/7091
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Gilda Ferreira - η-conversions of IPC implemented in atomic F. "Logic Journal of the IGPL" [Em linha]. ISSN 1367-0751 (Print) 1368-9894 (Online). Vol. 25, nº 2 (2017), p. 115–130
1367-0751 (Print)
10.1093/jigpal/jzw035
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 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:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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