A herbrandized functional interpretation of classical first-order logic
Autor(a) principal: | |
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Data de Publicação: | 2017 |
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/10400.2/7089 |
Resumo: | We introduce a new typed combinatory calculus with a type constructor that, to each type σ, associates the star type σ^∗ of the nonempty finite subsets of elements of type σ. We prove that this calculus enjoys the properties of strong normalization and confluence. With the aid of this star combinatory calculus, we define a functional interpretation of first-order predicate logic and prove a corresponding soundness theorem. It is seen that each theorem of classical first-order logic is connected with certain formulas which are tautological in character. As a corollary, we reprove Herbrand’s theorem on the extraction of terms from classically provable existential statements. |
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A herbrandized functional interpretation of classical first-order logicMathematical logicFunctional interpretationsFirst-order logicStar combinatory calculusFinite setsTautologiesHerbrand’s theoremWe introduce a new typed combinatory calculus with a type constructor that, to each type σ, associates the star type σ^∗ of the nonempty finite subsets of elements of type σ. We prove that this calculus enjoys the properties of strong normalization and confluence. With the aid of this star combinatory calculus, we define a functional interpretation of first-order predicate logic and prove a corresponding soundness theorem. It is seen that each theorem of classical first-order logic is connected with certain formulas which are tautological in character. As a corollary, we reprove Herbrand’s theorem on the extraction of terms from classically provable existential statements.SpringerRepositório AbertoFerreira, FernandoFerreira, Gilda2018-09-30T00:30:23Z20172017-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/7089engFerreira, Fernando; Ferreira, Gilda - A herbrandized functional interpretation of classical first-order logic. "Archive for Mathematical Logic" [Em linha]. ISSN 0933-5846 (Print) 1432-0665 (Online). Vol. 56, nº 5-6 (2017), p. 523-5390933-5846 (Print)10.1007/s00153-017-0555-6info: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:10400.2/7089Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:47:27.199885Repositório 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 |
A herbrandized functional interpretation of classical first-order logic |
title |
A herbrandized functional interpretation of classical first-order logic |
spellingShingle |
A herbrandized functional interpretation of classical first-order logic Ferreira, Fernando Mathematical logic Functional interpretations First-order logic Star combinatory calculus Finite sets Tautologies Herbrand’s theorem |
title_short |
A herbrandized functional interpretation of classical first-order logic |
title_full |
A herbrandized functional interpretation of classical first-order logic |
title_fullStr |
A herbrandized functional interpretation of classical first-order logic |
title_full_unstemmed |
A herbrandized functional interpretation of classical first-order logic |
title_sort |
A herbrandized functional interpretation of classical first-order logic |
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 |
Mathematical logic Functional interpretations First-order logic Star combinatory calculus Finite sets Tautologies Herbrand’s theorem |
topic |
Mathematical logic Functional interpretations First-order logic Star combinatory calculus Finite sets Tautologies Herbrand’s theorem |
description |
We introduce a new typed combinatory calculus with a type constructor that, to each type σ, associates the star type σ^∗ of the nonempty finite subsets of elements of type σ. We prove that this calculus enjoys the properties of strong normalization and confluence. With the aid of this star combinatory calculus, we define a functional interpretation of first-order predicate logic and prove a corresponding soundness theorem. It is seen that each theorem of classical first-order logic is connected with certain formulas which are tautological in character. As a corollary, we reprove Herbrand’s theorem on the extraction of terms from classically provable existential statements. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017 2017-01-01T00:00:00Z 2018-09-30T00:30:23Z |
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/10400.2/7089 |
url |
http://hdl.handle.net/10400.2/7089 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Ferreira, Fernando; Ferreira, Gilda - A herbrandized functional interpretation of classical first-order logic. "Archive for Mathematical Logic" [Em linha]. ISSN 0933-5846 (Print) 1432-0665 (Online). Vol. 56, nº 5-6 (2017), p. 523-539 0933-5846 (Print) 10.1007/s00153-017-0555-6 |
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 |
Springer |
publisher.none.fl_str_mv |
Springer |
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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1799135051189846016 |