Towards a canonical classical natural deduction system

Detalhes bibliográficos
Autor(a) principal: Espírito Santo, José
Data de Publicação: 2013
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: https://hdl.handle.net/1822/20939
Resumo: Preprint submitted to Elsevier, 6 July 2012
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spelling Towards a canonical classical natural deduction systemClassical logicSequent calculusNatural deductionControl operatorsLet-expressionsEta-reductionScience & TechnologyPreprint submitted to Elsevier, 6 July 2012This paper studies a new classical natural deduction system, presented as a typed calculus named lambda-mu- let. It is designed to be isomorphic to Curien and Herbelin's lambda-mu-mu~-calculus, both at the level of proofs and reduction, and the isomorphism is based on the correct correspondence between cut (resp. left-introduction) in sequent calculus, and substitution (resp. elimination) in natural deduction. It is a combination of Parigot's lambda-mu -calculus with the idea of "coercion calculus" due to Cervesato and Pfenning, accommodating let-expressions in a surprising way: they expand Parigot's syntactic class of named terms. This calculus and the mentioned isomorphism Theta offer three missing components of the proof theory of classical logic: a canonical natural deduction system; a robust process of "read-back" of calculi in the sequent calculus format into natural deduction syntax; a formalization of the usual semantics of the lambda-mu-mu~-calculus, that explains co-terms and cuts as, respectively, contexts and hole- filling instructions. lambda-mu-let is not yet another classical calculus, but rather a canonical reflection in natural deduction of the impeccable treatment of classical logic by sequent calculus; and provides the "read-back" map and the formalized semantics, based on the precise notions of context and "hole-expression" provided by lambda-mu-let. We use "read-back" to achieve a precise connection with Parigot's lambda-mu , and to derive lambda-calculi for call-by-value combining control and let-expressions in a logically founded way. Finally, the semantics , when fully developed, can be inverted at each syntactic category. This development gives us license to see sequent calculus as the semantics of natural deduction; and uncovers a new syntactic concept in lambda-mu-mu~ ("co-context"), with which one can give a new de nition of eta-reduction.Elsevier 1Universidade do MinhoEspírito Santo, José20132013-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/20939eng0168-007210.1016/j.apal.2012.05.008info: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:RCAAP2024-07-13T01:52:48Zoai:repositorium.sdum.uminho.pt:1822/20939Portal AgregadorONGhttps://www.rcaap.pt/oai/openairemluisa.alvim@gmail.comopendoar:71602024-07-13T01:52:48Repositório 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 Towards a canonical classical natural deduction system
title Towards a canonical classical natural deduction system
spellingShingle Towards a canonical classical natural deduction system
Espírito Santo, José
Classical logic
Sequent calculus
Natural deduction
Control operators
Let-expressions
Eta-reduction
Science & Technology
title_short Towards a canonical classical natural deduction system
title_full Towards a canonical classical natural deduction system
title_fullStr Towards a canonical classical natural deduction system
title_full_unstemmed Towards a canonical classical natural deduction system
title_sort Towards a canonical classical natural deduction system
author Espírito Santo, José
author_facet Espírito Santo, José
author_role author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Espírito Santo, José
dc.subject.por.fl_str_mv Classical logic
Sequent calculus
Natural deduction
Control operators
Let-expressions
Eta-reduction
Science & Technology
topic Classical logic
Sequent calculus
Natural deduction
Control operators
Let-expressions
Eta-reduction
Science & Technology
description Preprint submitted to Elsevier, 6 July 2012
publishDate 2013
dc.date.none.fl_str_mv 2013
2013-01-01T00:00:00Z
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 https://hdl.handle.net/1822/20939
url https://hdl.handle.net/1822/20939
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0168-0072
10.1016/j.apal.2012.05.008
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 Elsevier 1
publisher.none.fl_str_mv Elsevier 1
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
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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
repository.mail.fl_str_mv mluisa.alvim@gmail.com
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