Permutability of proofs in intuitionistic sequent calculi

Detalhes bibliográficos
Autor(a) principal: Pinto, Luís F.
Data de Publicação: 1999
Outros Autores: Dyckhoff, Roy
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/1822/3832
Resumo: We prove a folklore theorem, that two derivations in a cut-free sequent calculus for intuitionistic propositional logic (based on Kleene's {\bf G3}) are inter-permutable (using a set of basic "permutation reduction rules'' derived from Kleene's work in 1952) iff they determine the same natural deduction. The basic rules form a confluent and weakly normalising rewriting system. We refer to Schwichtenberg's proof elsewhere that a modification of this system is strongly normalising.
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spelling Permutability of proofs in intuitionistic sequent calculiIntuitionistic logicProof theoryNatural deductionSequent calculusScience & TechnologyWe prove a folklore theorem, that two derivations in a cut-free sequent calculus for intuitionistic propositional logic (based on Kleene's {\bf G3}) are inter-permutable (using a set of basic "permutation reduction rules'' derived from Kleene's work in 1952) iff they determine the same natural deduction. The basic rules form a confluent and weakly normalising rewriting system. We refer to Schwichtenberg's proof elsewhere that a modification of this system is strongly normalising.União Europeia (UE) - Programa ESPRIT BRA 7232 GENTZEN.Centro de Matemática da Universidade do Minho (CMAT).ElsevierUniversidade do MinhoPinto, Luís F.Dyckhoff, Roy19991999-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/postscriptapplication/pdfhttp://hdl.handle.net/1822/3832eng"Theoretical Computer Science". ISSN 0304-3975. 212:1/2 (1999) 141-155.0304-397510.1016/S0304-3975(98)00138-8The original publication is available at www.sciencedirect.cominfo: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:RCAAP2023-07-21T12:05:13Zoai:repositorium.sdum.uminho.pt:1822/3832Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T18:55:36.647871Repositório 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 Permutability of proofs in intuitionistic sequent calculi
title Permutability of proofs in intuitionistic sequent calculi
spellingShingle Permutability of proofs in intuitionistic sequent calculi
Pinto, Luís F.
Intuitionistic logic
Proof theory
Natural deduction
Sequent calculus
Science & Technology
title_short Permutability of proofs in intuitionistic sequent calculi
title_full Permutability of proofs in intuitionistic sequent calculi
title_fullStr Permutability of proofs in intuitionistic sequent calculi
title_full_unstemmed Permutability of proofs in intuitionistic sequent calculi
title_sort Permutability of proofs in intuitionistic sequent calculi
author Pinto, Luís F.
author_facet Pinto, Luís F.
Dyckhoff, Roy
author_role author
author2 Dyckhoff, Roy
author2_role author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Pinto, Luís F.
Dyckhoff, Roy
dc.subject.por.fl_str_mv Intuitionistic logic
Proof theory
Natural deduction
Sequent calculus
Science & Technology
topic Intuitionistic logic
Proof theory
Natural deduction
Sequent calculus
Science & Technology
description We prove a folklore theorem, that two derivations in a cut-free sequent calculus for intuitionistic propositional logic (based on Kleene's {\bf G3}) are inter-permutable (using a set of basic "permutation reduction rules'' derived from Kleene's work in 1952) iff they determine the same natural deduction. The basic rules form a confluent and weakly normalising rewriting system. We refer to Schwichtenberg's proof elsewhere that a modification of this system is strongly normalising.
publishDate 1999
dc.date.none.fl_str_mv 1999
1999-01-01T00:00:00Z
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/1822/3832
url http://hdl.handle.net/1822/3832
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv "Theoretical Computer Science". ISSN 0304-3975. 212:1/2 (1999) 141-155.
0304-3975
10.1016/S0304-3975(98)00138-8
The original publication is available at www.sciencedirect.com
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/postscript
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
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
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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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