Encoding de Finetti's coherence within Łukasiewicz logic and MV-algebras
The present paper investigates proof-theoretical and algebraic properties for the probability logic FP(Ł,Ł), meant for reasoning on the uncertainty of Łukasiewicz events. Methodologically speaking, we will consider a translation function between formulas of FP(Ł,Ł) to the propositional language of Ł...
| Autores: | , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2024 |
| País: | España |
| Recursos: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/378012 |
| Acesso em linha: | http://hdl.handle.net/10261/378012 |
| Access Level: | acceso abierto |
| Palavra-chave: | Probability logic Łukasiewicz logic MV-algebras De Finetti's coherence State theory |
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Encoding de Finetti's coherence within Łukasiewicz logic and MV-algebrasFlaminio, TommasoUgolini, SaraProbability logicŁukasiewicz logicMV-algebrasDe Finetti's coherenceState theoryThe present paper investigates proof-theoretical and algebraic properties for the probability logic FP(Ł,Ł), meant for reasoning on the uncertainty of Łukasiewicz events. Methodologically speaking, we will consider a translation function between formulas of FP(Ł,Ł) to the propositional language of Łukasiewicz logic that allows us to apply the latter and the well-developed theory of MV-algebras directly to probabilistic reasoning. More precisely, leveraging on such translation map, we will show proof-theoretical properties for FP(Ł,Ł) and introduce a class of algebras with respect to which FP(Ł,Ł) will be proved to be locally sound and complete. Finally, we will apply these previous results to investigate what we called “probabilistic unification problem”. In this respect, we will prove that Ghilardi’s algebraic view on unification can be extended to our case and, on par with the Łukasiewicz propositional case, we show that probabilistic unification is of nullary type.The authors acknowledge partial support by the MOSAIC project (H2020-MSCA-RISE-2020 Project 101007627). Ugolini acknowledges support from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 890616 (H2020-MSCA-IF-2019) and the Ramón y Cajal programme RyC2021-032670-I.Peer reviewedElsevierEuropean CommissionAgencia Estatal de Investigación (España)Ministerio de Ciencia e Innovación (España)Flaminio, Tommaso [0000-0002-9180-7808]Ugolini, Sara [0000-0002-8663-042X]Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]202520252024info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Publisher's versioninfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/10261/378012reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Inglés#PLACEHOLDER_PARENT_METADATA_VALUE##PLACEHOLDER_PARENT_METADATA_VALUE##PLACEHOLDER_PARENT_METADATA_VALUE#info:eu-repo/grantAgreement/EC/H2020/101007627info:eu-repo/grantAgreement/EC/H2020/890616info:eu-repo/grantAgreement/AEI//RyC2021-032670-Ihttps://doi.org/10.1016/j.apal.2023.103337Síinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/3780122026-05-22T06:33:51Z |
| dc.title.none.fl_str_mv |
Encoding de Finetti's coherence within Łukasiewicz logic and MV-algebras |
| title |
Encoding de Finetti's coherence within Łukasiewicz logic and MV-algebras |
| spellingShingle |
Encoding de Finetti's coherence within Łukasiewicz logic and MV-algebras Flaminio, Tommaso Probability logic Łukasiewicz logic MV-algebras De Finetti's coherence State theory |
| title_short |
Encoding de Finetti's coherence within Łukasiewicz logic and MV-algebras |
| title_full |
Encoding de Finetti's coherence within Łukasiewicz logic and MV-algebras |
| title_fullStr |
Encoding de Finetti's coherence within Łukasiewicz logic and MV-algebras |
| title_full_unstemmed |
Encoding de Finetti's coherence within Łukasiewicz logic and MV-algebras |
| title_sort |
Encoding de Finetti's coherence within Łukasiewicz logic and MV-algebras |
| dc.creator.none.fl_str_mv |
Flaminio, Tommaso Ugolini, Sara |
| author |
Flaminio, Tommaso |
| author_facet |
Flaminio, Tommaso Ugolini, Sara |
| author_role |
author |
| author2 |
Ugolini, Sara |
| author2_role |
author |
| dc.contributor.none.fl_str_mv |
European Commission Agencia Estatal de Investigación (España) Ministerio de Ciencia e Innovación (España) Flaminio, Tommaso [0000-0002-9180-7808] Ugolini, Sara [0000-0002-8663-042X] Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72] |
| dc.subject.none.fl_str_mv |
Probability logic Łukasiewicz logic MV-algebras De Finetti's coherence State theory |
| topic |
Probability logic Łukasiewicz logic MV-algebras De Finetti's coherence State theory |
| description |
The present paper investigates proof-theoretical and algebraic properties for the probability logic FP(Ł,Ł), meant for reasoning on the uncertainty of Łukasiewicz events. Methodologically speaking, we will consider a translation function between formulas of FP(Ł,Ł) to the propositional language of Łukasiewicz logic that allows us to apply the latter and the well-developed theory of MV-algebras directly to probabilistic reasoning. More precisely, leveraging on such translation map, we will show proof-theoretical properties for FP(Ł,Ł) and introduce a class of algebras with respect to which FP(Ł,Ł) will be proved to be locally sound and complete. Finally, we will apply these previous results to investigate what we called “probabilistic unification problem”. In this respect, we will prove that Ghilardi’s algebraic view on unification can be extended to our case and, on par with the Łukasiewicz propositional case, we show that probabilistic unification is of nullary type. |
| publishDate |
2024 |
| dc.date.none.fl_str_mv |
2024 2025 2025 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/article http://purl.org/coar/resource_type/c_6501 Publisher's version info:eu-repo/semantics/publishedVersion |
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article |
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publishedVersion |
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http://hdl.handle.net/10261/378012 |
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http://hdl.handle.net/10261/378012 |
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Inglés |
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Inglés |
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#PLACEHOLDER_PARENT_METADATA_VALUE# #PLACEHOLDER_PARENT_METADATA_VALUE# #PLACEHOLDER_PARENT_METADATA_VALUE# info:eu-repo/grantAgreement/EC/H2020/101007627 info:eu-repo/grantAgreement/EC/H2020/890616 info:eu-repo/grantAgreement/AEI//RyC2021-032670-I https://doi.org/10.1016/j.apal.2023.103337 Sí |
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info:eu-repo/semantics/openAccess |
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openAccess |
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application/pdf |
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Elsevier |
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Elsevier |
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reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC instname:Consejo Superior de Investigaciones Científicas (CSIC) |
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