Convergence: what’s logic got to do with it?
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Tipo de documento: | Artigo de conferência |
Idioma: | por |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10174/33645 |
Resumo: | Proof mining is a program that makes use of tools from mathematical logic in order to analyse mathematical proofs. This analysis is developed with the purpose of extracting quantitative information from proofs, for example in the form of effective bounds and/or algorithms. The success of the proof mining program is due to the ability of extracting computational content from non-constructive proofs which often allows to improve the results analysed by weakening the hypotheses necessary to prove them. Moreover, in the improved results the logical tools used to analyse the original proof are not visible and can therefore be read by non-logicians. Nevertheless, the understanding of certain logical principles, as well as their strength, is crucial in order to perform the extraction of information from the proof. In this talk I will give a soft introduction to the proof mining program focusing on the somewhat simple example of the convergence of sequences. As it turns out, this is a very fruitful example, related with Terence Tao’s notion of metastability, which is has been paramount in different areas of research. |
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Convergence: what’s logic got to do with it?Proof miningconvergenceProof mining is a program that makes use of tools from mathematical logic in order to analyse mathematical proofs. This analysis is developed with the purpose of extracting quantitative information from proofs, for example in the form of effective bounds and/or algorithms. The success of the proof mining program is due to the ability of extracting computational content from non-constructive proofs which often allows to improve the results analysed by weakening the hypotheses necessary to prove them. Moreover, in the improved results the logical tools used to analyse the original proof are not visible and can therefore be read by non-logicians. Nevertheless, the understanding of certain logical principles, as well as their strength, is crucial in order to perform the extraction of information from the proof. In this talk I will give a soft introduction to the proof mining program focusing on the somewhat simple example of the convergence of sequences. As it turns out, this is a very fruitful example, related with Terence Tao’s notion of metastability, which is has been paramount in different areas of research.2023-01-25T15:37:02Z2023-01-252022-11-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/conferenceObjecthttp://hdl.handle.net/10174/33645http://hdl.handle.net/10174/33645porhttps://www.cima.uevora.pt/attachments/article/169/Seminario_BrunoDinis.pdfsimnaonaoCIMAbruno.dinis@uevora.ptDinis, Brunoinfo: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:RCAAP2024-01-03T19:35:34Zoai:dspace.uevora.pt:10174/33645Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T01:22:24.054102Repositório 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 |
Convergence: what’s logic got to do with it? |
title |
Convergence: what’s logic got to do with it? |
spellingShingle |
Convergence: what’s logic got to do with it? Dinis, Bruno Proof mining convergence |
title_short |
Convergence: what’s logic got to do with it? |
title_full |
Convergence: what’s logic got to do with it? |
title_fullStr |
Convergence: what’s logic got to do with it? |
title_full_unstemmed |
Convergence: what’s logic got to do with it? |
title_sort |
Convergence: what’s logic got to do with it? |
author |
Dinis, Bruno |
author_facet |
Dinis, Bruno |
author_role |
author |
dc.contributor.author.fl_str_mv |
Dinis, Bruno |
dc.subject.por.fl_str_mv |
Proof mining convergence |
topic |
Proof mining convergence |
description |
Proof mining is a program that makes use of tools from mathematical logic in order to analyse mathematical proofs. This analysis is developed with the purpose of extracting quantitative information from proofs, for example in the form of effective bounds and/or algorithms. The success of the proof mining program is due to the ability of extracting computational content from non-constructive proofs which often allows to improve the results analysed by weakening the hypotheses necessary to prove them. Moreover, in the improved results the logical tools used to analyse the original proof are not visible and can therefore be read by non-logicians. Nevertheless, the understanding of certain logical principles, as well as their strength, is crucial in order to perform the extraction of information from the proof. In this talk I will give a soft introduction to the proof mining program focusing on the somewhat simple example of the convergence of sequences. As it turns out, this is a very fruitful example, related with Terence Tao’s notion of metastability, which is has been paramount in different areas of research. |
publishDate |
2022 |
dc.date.none.fl_str_mv |
2022-11-01T00:00:00Z 2023-01-25T15:37:02Z 2023-01-25 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
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info:eu-repo/semantics/conferenceObject |
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conferenceObject |
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publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10174/33645 http://hdl.handle.net/10174/33645 |
url |
http://hdl.handle.net/10174/33645 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.none.fl_str_mv |
https://www.cima.uevora.pt/attachments/article/169/Seminario_BrunoDinis.pdf sim nao nao CIMA bruno.dinis@uevora.pt |
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info:eu-repo/semantics/openAccess |
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openAccess |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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