The faithfulness of Fat: a proof-theoretic proof

Detalhes bibliográficos
Autor(a) principal: Ferreira, Fernando
Data de Publicação: 2015
Outros Autores: Ferreira, Gilda
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.2/10490
Resumo: It is known that there is a sound and faithful translation of the full intuitionistic propositional calculus into the atomic polymorphic system Fat, a predicative calculus with only two connectives: the conditional and the second-order universal quantifier. The faithfulness of the embedding was established quite recently via a model-theoretic argument based in Kripke structures. In this paper we present a purely proof-theoretic proof of faithfulness. As an application, we give a purely proof-theoretic proof of the disjunction property of the intuitionistic propositional logic in which commuting conversions are not needed.
id RCAP_f793aafafede557453c8cd79f7a648df
oai_identifier_str oai:repositorioaberto.uab.pt:10400.2/10490
network_acronym_str RCAP
network_name_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository_id_str
spelling The faithfulness of Fat: a proof-theoretic proofPredicative polymorphismFaithfulnessNatural deductionIntuitionistic proposicional calculusDisjunction propertyStrong normalizationIt is known that there is a sound and faithful translation of the full intuitionistic propositional calculus into the atomic polymorphic system Fat, a predicative calculus with only two connectives: the conditional and the second-order universal quantifier. The faithfulness of the embedding was established quite recently via a model-theoretic argument based in Kripke structures. In this paper we present a purely proof-theoretic proof of faithfulness. As an application, we give a purely proof-theoretic proof of the disjunction property of the intuitionistic propositional logic in which commuting conversions are not needed.Repositório AbertoFerreira, FernandoFerreira, Gilda2021-02-15T10:00:38Z20152015-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/10490eng0039-321510.1007/s11225-015-9620-5info: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:RCAAP2023-07-07T16:10:20ZPortal AgregadorONG
dc.title.none.fl_str_mv The faithfulness of Fat: a proof-theoretic proof
title The faithfulness of Fat: a proof-theoretic proof
spellingShingle The faithfulness of Fat: a proof-theoretic proof
Ferreira, Fernando
Predicative polymorphism
Faithfulness
Natural deduction
Intuitionistic proposicional calculus
Disjunction property
Strong normalization
title_short The faithfulness of Fat: a proof-theoretic proof
title_full The faithfulness of Fat: a proof-theoretic proof
title_fullStr The faithfulness of Fat: a proof-theoretic proof
title_full_unstemmed The faithfulness of Fat: a proof-theoretic proof
title_sort The faithfulness of Fat: a proof-theoretic proof
author Ferreira, Fernando
author_facet Ferreira, Fernando
Ferreira, Gilda
author_role author
author2 Ferreira, Gilda
author2_role author
dc.contributor.none.fl_str_mv Repositório Aberto
dc.contributor.author.fl_str_mv Ferreira, Fernando
Ferreira, Gilda
dc.subject.por.fl_str_mv Predicative polymorphism
Faithfulness
Natural deduction
Intuitionistic proposicional calculus
Disjunction property
Strong normalization
topic Predicative polymorphism
Faithfulness
Natural deduction
Intuitionistic proposicional calculus
Disjunction property
Strong normalization
description It is known that there is a sound and faithful translation of the full intuitionistic propositional calculus into the atomic polymorphic system Fat, a predicative calculus with only two connectives: the conditional and the second-order universal quantifier. The faithfulness of the embedding was established quite recently via a model-theoretic argument based in Kripke structures. In this paper we present a purely proof-theoretic proof of faithfulness. As an application, we give a purely proof-theoretic proof of the disjunction property of the intuitionistic propositional logic in which commuting conversions are not needed.
publishDate 2015
dc.date.none.fl_str_mv 2015
2015-01-01T00:00:00Z
2021-02-15T10:00:38Z
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/10400.2/10490
url http://hdl.handle.net/10400.2/10490
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0039-3215
10.1007/s11225-015-9620-5
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.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
repository.mail.fl_str_mv
_version_ 1777302857033187328

Registros relacionados