On conditional probabilities and their canonical extensions to Boolean algebras of compound conditionals

[Data availability] No data was used for the research described in the article.

Detalhes bibliográficos
Autores: Flaminio, Tommaso, Gilio, Angelo, Godo, Lluis, Sanfilippo, Giuseppe
Tipo de documento: artigo
Estado:Versão publicada
Data de publicação:2023
País:España
Recursos:Consejo Superior de Investigaciones Científicas (CSIC)
Repositório:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/404556
Acesso em linha:http://hdl.handle.net/10261/404556
https://api.elsevier.com/content/abstract/scopus_id/85160411990
Access Level:Acceso aberto
Palavra-chave:Boolean algebras of conditionals
Canonical extension
Conditional probability
Conditional subalgebras
Conjunction and disjunction of conditionals
Nonmonotonic reasoning
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spelling On conditional probabilities and their canonical extensions to Boolean algebras of compound conditionalsFlaminio, TommasoGilio, AngeloGodo, LluisSanfilippo, GiuseppeBoolean algebras of conditionalsCanonical extensionConditional probabilityConditional subalgebrasConjunction and disjunction of conditionalsNonmonotonic reasoning[Data availability] No data was used for the research described in the article.In this paper we investigate canonical extensions of conditional probabilities to Boolean algebras of conditionals. Before entering into the probabilistic setting, we first prove that the lattice order relation of every Boolean algebra of conditionals can be characterized in terms of the well-known order relation given by Goodman and Nguyen. Then, as an interesting methodological tool, we show that canonical extensions behave well with respect to conditional subalgebras. As a consequence, we prove that a canonical extension and its original conditional probability agree on basic conditionals. Moreover, we verify that the probability of conjunctions and disjunctions of conditionals in a recently introduced framework of Boolean algebras of conditionals are in full agreement with the corresponding operations of conditionals as defined in the approach developed by two of the authors to conditionals as three-valued objects, with betting-based semantics, and specified as suitable random quantities. Finally we discuss relations of our approach with nonmonotonic reasoning based on an entailment relation among conditionals.The authors are grateful to the anonymous reviewers for their helpful comments and suggestions. Flaminio and Godo acknowledge partial support by the MOSAIC project (EU H2020-MSCA-RISE-2020 Project 101007627) and also by the Spanish project PID2019-111544GB-C21/AEI/10.13039/501100011033. Sanfilippo acknowledges support by the FFR 2023 project of University of Palermo, Italy.Peer reviewedElsevier BVEuropean CommissionAgencia Estatal de Investigación (España)Ministerio de Ciencia, Innovación y Universidades (España)Università degli Studi di PalermoFlaminio, Tommaso [0000-0002-9180-7808]Godo, Lluis [0000-0002-6929-3126]Sanfilippo, Giuseppe [0000-0002-0657-3833]Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]202520252023info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Publisher's versioninfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/10261/404556https://api.elsevier.com/content/abstract/scopus_id/85160411990reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Inglés#PLACEHOLDER_PARENT_METADATA_VALUE##PLACEHOLDER_PARENT_METADATA_VALUE#info:eu-repo/grantAgreement/EC/H2020/101007627info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-111544GB-C21https://doi.org/10.1016/j.ijar.2023.108943Síinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/4045562026-05-22T06:33:51Z
dc.title.none.fl_str_mv On conditional probabilities and their canonical extensions to Boolean algebras of compound conditionals
title On conditional probabilities and their canonical extensions to Boolean algebras of compound conditionals
spellingShingle On conditional probabilities and their canonical extensions to Boolean algebras of compound conditionals
Flaminio, Tommaso
Boolean algebras of conditionals
Canonical extension
Conditional probability
Conditional subalgebras
Conjunction and disjunction of conditionals
Nonmonotonic reasoning
title_short On conditional probabilities and their canonical extensions to Boolean algebras of compound conditionals
title_full On conditional probabilities and their canonical extensions to Boolean algebras of compound conditionals
title_fullStr On conditional probabilities and their canonical extensions to Boolean algebras of compound conditionals
title_full_unstemmed On conditional probabilities and their canonical extensions to Boolean algebras of compound conditionals
title_sort On conditional probabilities and their canonical extensions to Boolean algebras of compound conditionals
dc.creator.none.fl_str_mv Flaminio, Tommaso
Gilio, Angelo
Godo, Lluis
Sanfilippo, Giuseppe
author Flaminio, Tommaso
author_facet Flaminio, Tommaso
Gilio, Angelo
Godo, Lluis
Sanfilippo, Giuseppe
author_role author
author2 Gilio, Angelo
Godo, Lluis
Sanfilippo, Giuseppe
author2_role author
author
author
dc.contributor.none.fl_str_mv European Commission
Agencia Estatal de Investigación (España)
Ministerio de Ciencia, Innovación y Universidades (España)
Università degli Studi di Palermo
Flaminio, Tommaso [0000-0002-9180-7808]
Godo, Lluis [0000-0002-6929-3126]
Sanfilippo, Giuseppe [0000-0002-0657-3833]
Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
dc.subject.none.fl_str_mv Boolean algebras of conditionals
Canonical extension
Conditional probability
Conditional subalgebras
Conjunction and disjunction of conditionals
Nonmonotonic reasoning
topic Boolean algebras of conditionals
Canonical extension
Conditional probability
Conditional subalgebras
Conjunction and disjunction of conditionals
Nonmonotonic reasoning
description [Data availability] No data was used for the research described in the article.
publishDate 2023
dc.date.none.fl_str_mv 2023
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
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/404556
https://api.elsevier.com/content/abstract/scopus_id/85160411990
url http://hdl.handle.net/10261/404556
https://api.elsevier.com/content/abstract/scopus_id/85160411990
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
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info:eu-repo/grantAgreement/EC/H2020/101007627
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-111544GB-C21
https://doi.org/10.1016/j.ijar.2023.108943
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eu_rights_str_mv openAccess
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dc.publisher.none.fl_str_mv Elsevier BV
publisher.none.fl_str_mv Elsevier BV
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