The Russell-Prawitz embedding and the atomization of universal instantiation
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.2/10493 |
Resumo: | Given the recent interest in the fragment of system F where universal instantiation is restricted to atomic formulas, a fragment nowadays named system Fat, we study directly in system F new conversions whose purpose is to enforce that restriction. We show some benefits of these new atomization conversions: (1) They help achieving strict simulation of proof reduction by means of the Russell-Prawitz embedding of IPC into system F; (2) They are not stronger than a certain “dinaturality” conversion known to generate a consistent equality of proofs; (3) They provide the bridge between the Russell-Prawitz embedding and another translation, due to the authors, of IPC directly into system Fat; (4) They give means for explaining why the Russell-Prawitz translation achieves strict simulation whereas the translation into Fat does not. |
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The Russell-Prawitz embedding and the atomization of universal instantiationIntuitionistic propositional calculusSystem FPredicative polymorphismRussell-Prawitz translationProof reductionGiven the recent interest in the fragment of system F where universal instantiation is restricted to atomic formulas, a fragment nowadays named system Fat, we study directly in system F new conversions whose purpose is to enforce that restriction. We show some benefits of these new atomization conversions: (1) They help achieving strict simulation of proof reduction by means of the Russell-Prawitz embedding of IPC into system F; (2) They are not stronger than a certain “dinaturality” conversion known to generate a consistent equality of proofs; (3) They provide the bridge between the Russell-Prawitz embedding and another translation, due to the authors, of IPC directly into system Fat; (4) They give means for explaining why the Russell-Prawitz translation achieves strict simulation whereas the translation into Fat does not.Oxford AcademicRepositório AbertoEspírito Santo, JoséFerreira, Gilda2022-02-01T01:30:29Z20202020-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/10493eng1367-075110.1093/jigpal/jzaa0251368-9894info: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:RCAAP2023-11-16T15:35:37Zoai:repositorioaberto.uab.pt:10400.2/10493Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:50:03.541783Repositório 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 |
The Russell-Prawitz embedding and the atomization of universal instantiation |
title |
The Russell-Prawitz embedding and the atomization of universal instantiation |
spellingShingle |
The Russell-Prawitz embedding and the atomization of universal instantiation Espírito Santo, José Intuitionistic propositional calculus System F Predicative polymorphism Russell-Prawitz translation Proof reduction |
title_short |
The Russell-Prawitz embedding and the atomization of universal instantiation |
title_full |
The Russell-Prawitz embedding and the atomization of universal instantiation |
title_fullStr |
The Russell-Prawitz embedding and the atomization of universal instantiation |
title_full_unstemmed |
The Russell-Prawitz embedding and the atomization of universal instantiation |
title_sort |
The Russell-Prawitz embedding and the atomization of universal instantiation |
author |
Espírito Santo, José |
author_facet |
Espírito Santo, José 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 |
Espírito Santo, José Ferreira, Gilda |
dc.subject.por.fl_str_mv |
Intuitionistic propositional calculus System F Predicative polymorphism Russell-Prawitz translation Proof reduction |
topic |
Intuitionistic propositional calculus System F Predicative polymorphism Russell-Prawitz translation Proof reduction |
description |
Given the recent interest in the fragment of system F where universal instantiation is restricted to atomic formulas, a fragment nowadays named system Fat, we study directly in system F new conversions whose purpose is to enforce that restriction. We show some benefits of these new atomization conversions: (1) They help achieving strict simulation of proof reduction by means of the Russell-Prawitz embedding of IPC into system F; (2) They are not stronger than a certain “dinaturality” conversion known to generate a consistent equality of proofs; (3) They provide the bridge between the Russell-Prawitz embedding and another translation, due to the authors, of IPC directly into system Fat; (4) They give means for explaining why the Russell-Prawitz translation achieves strict simulation whereas the translation into Fat does not. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020 2020-01-01T00:00:00Z 2022-02-01T01:30:29Z |
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/10400.2/10493 |
url |
http://hdl.handle.net/10400.2/10493 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1367-0751 10.1093/jigpal/jzaa025 1368-9894 |
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 Academic |
publisher.none.fl_str_mv |
Oxford Academic |
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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1817551272837906432 |