Towards a canonical classical natural deduction system
Autor(a) principal: | |
---|---|
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 |
id |
RCAP_135e39b58104b41eae942d825abea849 |
---|---|
oai_identifier_str |
oai:repositorium.sdum.uminho.pt:1822/20939 |
network_acronym_str |
RCAP |
network_name_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository_id_str |
7160 |
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 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 |
mluisa.alvim@gmail.com |
_version_ |
1817544231800012800 |