Boolean algebras of conditionals, probability and logic

This paper presents an investigation on the structure of conditional events and on the probability measures which arise naturally in that context. In particular we introduce a construction which defines a (finite) Boolean algebra of conditionals from any (finite) Boolean algebra of events. By doing...

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Detalles Bibliográficos
Autores: Flaminio, Tommaso, Godo, Lluis, Hosni, Hykel
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2020
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/234595
Acceso en línea:http://hdl.handle.net/10261/234595
https://doi.org/10.1016/j.artint.2020.103347
Access Level:acceso abierto
Palabra clave:Conditional probability
Conditional events
Boolean algebra
Preferential consequence relations
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spelling Boolean algebras of conditionals, probability and logicFlaminio, TommasoGodo, LluisHosni, HykelConditional probabilityConditional eventsBoolean algebraPreferential consequence relationsThis paper presents an investigation on the structure of conditional events and on the probability measures which arise naturally in that context. In particular we introduce a construction which defines a (finite) Boolean algebra of conditionals from any (finite) Boolean algebra of events. By doing so we distinguish the properties of conditional events which depend on probability and those which are intrinsic to the logico-algebraic structure of conditionals. Our main result provides a way to regard standard two-place conditional probabilities as one-place probability functions on conditional events. We also consider a logical counterpart of our Boolean algebras of conditionals with links to preferential consequence relations for non-monotonic reasoning. The overall framework of this paper provides a novel perspective on the rich interplay between logic and probability in the representation of conditional knowledge.Flaminio and Godo acknowledge partial support by the Spanish FEDER/MINECO project TIN2015-71799-C2-1-P. Flaminio also acknowledges partial support by the Spanish Ramón y Cajal research program RYC-2016-19799. Hosni acknowledges funding from the Department of Philosophy “Piero Martinetti” of the University of Milan under the project “Departments of Excellence 2018-2022”, awarded by the Ministry of Education, University and Research (MIUR). He also acknowledges funding from the Deutsche Forschungsgemeinschaft (DFG, grant LA 4093/3-1)Elsevier BVMinisterio de Ciencia e Innovación (España)Ministero dell'Istruzione, dell'Università e della RicercaGerman Research FoundationConsejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]2021202120202021info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Postprintinfo:eu-repo/semantics/acceptedVersionhttp://hdl.handle.net/10261/234595https://doi.org/10.1016/j.artint.2020.103347reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Ingléshttp://dx.doi.org/10.1016/j.artint.2020.103347Síinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/2345952026-05-22T06:33:51Z
dc.title.none.fl_str_mv Boolean algebras of conditionals, probability and logic
title Boolean algebras of conditionals, probability and logic
spellingShingle Boolean algebras of conditionals, probability and logic
Flaminio, Tommaso
Conditional probability
Conditional events
Boolean algebra
Preferential consequence relations
title_short Boolean algebras of conditionals, probability and logic
title_full Boolean algebras of conditionals, probability and logic
title_fullStr Boolean algebras of conditionals, probability and logic
title_full_unstemmed Boolean algebras of conditionals, probability and logic
title_sort Boolean algebras of conditionals, probability and logic
dc.creator.none.fl_str_mv Flaminio, Tommaso
Godo, Lluis
Hosni, Hykel
author Flaminio, Tommaso
author_facet Flaminio, Tommaso
Godo, Lluis
Hosni, Hykel
author_role author
author2 Godo, Lluis
Hosni, Hykel
author2_role author
author
dc.contributor.none.fl_str_mv Ministerio de Ciencia e Innovación (España)
Ministero dell'Istruzione, dell'Università e della Ricerca
German Research Foundation
Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
dc.subject.none.fl_str_mv Conditional probability
Conditional events
Boolean algebra
Preferential consequence relations
topic Conditional probability
Conditional events
Boolean algebra
Preferential consequence relations
description This paper presents an investigation on the structure of conditional events and on the probability measures which arise naturally in that context. In particular we introduce a construction which defines a (finite) Boolean algebra of conditionals from any (finite) Boolean algebra of events. By doing so we distinguish the properties of conditional events which depend on probability and those which are intrinsic to the logico-algebraic structure of conditionals. Our main result provides a way to regard standard two-place conditional probabilities as one-place probability functions on conditional events. We also consider a logical counterpart of our Boolean algebras of conditionals with links to preferential consequence relations for non-monotonic reasoning. The overall framework of this paper provides a novel perspective on the rich interplay between logic and probability in the representation of conditional knowledge.
publishDate 2020
dc.date.none.fl_str_mv 2020
2021
2021
2021
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
Postprint
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/234595
https://doi.org/10.1016/j.artint.2020.103347
url http://hdl.handle.net/10261/234595
https://doi.org/10.1016/j.artint.2020.103347
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv http://dx.doi.org/10.1016/j.artint.2020.103347
Sí
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Elsevier BV
publisher.none.fl_str_mv Elsevier BV
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
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repository.mail.fl_str_mv
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