From cut-free calculi to automated deduction: the case of bounded contraction
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFRN |
Texto Completo: | https://repositorio.ufrn.br/jspui/handle/123456789/29757 |
Resumo: | The addition of the bounded contraction rules to Full Lambek Calculus with exchange and weakening (FLew) gives rise to serious complications for proof search. For example, adding to FLew a naive version of these rules brakes cut-admissibility. Although this can be avoided by refining these rules, in this work we show that even “good” proof systems for FLew plus bounded contraction do not necessarily lead to good implementations. In order to solve this problem, we propose an extension of the lazy splitting methodology to bounded contractions, showing how to transform our focused, cut-free sequent calculus into a terminating theorem prover. Our system is used to show that the decision problem for FLew with bounded contraction is in EXPTIME |
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Ciabattoni, AgataLellmann, BjornVega, Carlos Alberto OlartePimentel, Elaine Gouvea2020-07-30T18:37:21Z2020-07-30T18:37:21Z2017CIABATTONI, Agata; LELLMANN, Björn; OLARTE, Carlos; PIMENTEL, Elaine. From Cut-free Calculi to Automated Deduction: the case of bounded contraction. Electronic Notes in Theoretical Computer Science, [S.L.], v. 332, p. 75-93, jun. 2017. Disponível em: https://www.researchgate.net/publication/317825238_From_Cut-free_Calculi_to_Automated_Deduction_The_Case_of_Bounded_Contraction. Acesso em: 29 jul. 2020. http://dx.doi.org/10.1016/j.entcs.2017.04.006.1571-0661https://repositorio.ufrn.br/jspui/handle/123456789/2975710.1016/j.entcs.2017.04.006.ElsevierProof theorySubstructural logicsProof searchBounded contractionFrom cut-free calculi to automated deduction: the case of bounded contractioninfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleThe addition of the bounded contraction rules to Full Lambek Calculus with exchange and weakening (FLew) gives rise to serious complications for proof search. For example, adding to FLew a naive version of these rules brakes cut-admissibility. Although this can be avoided by refining these rules, in this work we show that even “good” proof systems for FLew plus bounded contraction do not necessarily lead to good implementations. In order to solve this problem, we propose an extension of the lazy splitting methodology to bounded contractions, showing how to transform our focused, cut-free sequent calculus into a terminating theorem prover. Our system is used to show that the decision problem for FLew with bounded contraction is in EXPTIMEengreponame:Repositório Institucional da UFRNinstname:Universidade Federal do Rio Grande do Norte (UFRN)instacron:UFRNinfo:eu-repo/semantics/openAccessORIGINALFromCut-freeCalculi_VEGA_2017.pdfFromCut-freeCalculi_VEGA_2017.pdfapplication/pdf331968https://repositorio.ufrn.br/bitstream/123456789/29757/1/FromCut-freeCalculi_VEGA_2017.pdf4dc556ed161e60cf550e71200fffb88aMD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81484https://repositorio.ufrn.br/bitstream/123456789/29757/2/license.txte9597aa2854d128fd968be5edc8a28d9MD52TEXTFromCut-freeCalculi_VEGA_2017.pdf.txtFromCut-freeCalculi_VEGA_2017.pdf.txtExtracted texttext/plain49542https://repositorio.ufrn.br/bitstream/123456789/29757/3/FromCut-freeCalculi_VEGA_2017.pdf.txt1a78d793509f5a22b51175f5903bef44MD53THUMBNAILFromCut-freeCalculi_VEGA_2017.pdf.jpgFromCut-freeCalculi_VEGA_2017.pdf.jpgGenerated Thumbnailimage/jpeg1532https://repositorio.ufrn.br/bitstream/123456789/29757/4/FromCut-freeCalculi_VEGA_2017.pdf.jpg2a36c70fc202bd8a8e60061ade72da7bMD54123456789/297572020-08-02 04:54:42.554oai:https://repositorio.ufrn.br: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Repositório de PublicaçõesPUBhttp://repositorio.ufrn.br/oai/opendoar:2020-08-02T07:54:42Repositório Institucional da UFRN - Universidade Federal do Rio Grande do Norte (UFRN)false |
dc.title.pt_BR.fl_str_mv |
From cut-free calculi to automated deduction: the case of bounded contraction |
title |
From cut-free calculi to automated deduction: the case of bounded contraction |
spellingShingle |
From cut-free calculi to automated deduction: the case of bounded contraction Ciabattoni, Agata Proof theory Substructural logics Proof search Bounded contraction |
title_short |
From cut-free calculi to automated deduction: the case of bounded contraction |
title_full |
From cut-free calculi to automated deduction: the case of bounded contraction |
title_fullStr |
From cut-free calculi to automated deduction: the case of bounded contraction |
title_full_unstemmed |
From cut-free calculi to automated deduction: the case of bounded contraction |
title_sort |
From cut-free calculi to automated deduction: the case of bounded contraction |
author |
Ciabattoni, Agata |
author_facet |
Ciabattoni, Agata Lellmann, Bjorn Vega, Carlos Alberto Olarte Pimentel, Elaine Gouvea |
author_role |
author |
author2 |
Lellmann, Bjorn Vega, Carlos Alberto Olarte Pimentel, Elaine Gouvea |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Ciabattoni, Agata Lellmann, Bjorn Vega, Carlos Alberto Olarte Pimentel, Elaine Gouvea |
dc.subject.por.fl_str_mv |
Proof theory Substructural logics Proof search Bounded contraction |
topic |
Proof theory Substructural logics Proof search Bounded contraction |
description |
The addition of the bounded contraction rules to Full Lambek Calculus with exchange and weakening (FLew) gives rise to serious complications for proof search. For example, adding to FLew a naive version of these rules brakes cut-admissibility. Although this can be avoided by refining these rules, in this work we show that even “good” proof systems for FLew plus bounded contraction do not necessarily lead to good implementations. In order to solve this problem, we propose an extension of the lazy splitting methodology to bounded contractions, showing how to transform our focused, cut-free sequent calculus into a terminating theorem prover. Our system is used to show that the decision problem for FLew with bounded contraction is in EXPTIME |
publishDate |
2017 |
dc.date.issued.fl_str_mv |
2017 |
dc.date.accessioned.fl_str_mv |
2020-07-30T18:37:21Z |
dc.date.available.fl_str_mv |
2020-07-30T18:37:21Z |
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.citation.fl_str_mv |
CIABATTONI, Agata; LELLMANN, Björn; OLARTE, Carlos; PIMENTEL, Elaine. From Cut-free Calculi to Automated Deduction: the case of bounded contraction. Electronic Notes in Theoretical Computer Science, [S.L.], v. 332, p. 75-93, jun. 2017. Disponível em: https://www.researchgate.net/publication/317825238_From_Cut-free_Calculi_to_Automated_Deduction_The_Case_of_Bounded_Contraction. Acesso em: 29 jul. 2020. http://dx.doi.org/10.1016/j.entcs.2017.04.006. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufrn.br/jspui/handle/123456789/29757 |
dc.identifier.issn.none.fl_str_mv |
1571-0661 |
dc.identifier.doi.none.fl_str_mv |
10.1016/j.entcs.2017.04.006. |
identifier_str_mv |
CIABATTONI, Agata; LELLMANN, Björn; OLARTE, Carlos; PIMENTEL, Elaine. From Cut-free Calculi to Automated Deduction: the case of bounded contraction. Electronic Notes in Theoretical Computer Science, [S.L.], v. 332, p. 75-93, jun. 2017. Disponível em: https://www.researchgate.net/publication/317825238_From_Cut-free_Calculi_to_Automated_Deduction_The_Case_of_Bounded_Contraction. Acesso em: 29 jul. 2020. http://dx.doi.org/10.1016/j.entcs.2017.04.006. 1571-0661 10.1016/j.entcs.2017.04.006. |
url |
https://repositorio.ufrn.br/jspui/handle/123456789/29757 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
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openAccess |
dc.publisher.none.fl_str_mv |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UFRN instname:Universidade Federal do Rio Grande do Norte (UFRN) instacron:UFRN |
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