η-conversions of IPC implemented in atomic F
Autor(a) principal: | |
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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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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 |
repository.mail.fl_str_mv |
|
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1817553901806682113 |