On Boolean Algebras of Conditionals and Their Logical Counterpart

This paper sheds a novel light on the longstanding problem of investigating the logic of conditional events. Building on the framework of Boolean algebras of conditionals previously introduced by the authors, we make two main new contributions. First, we fully characterise the atomic structure of th...

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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:2017
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/164664
Acceso en línea:http://hdl.handle.net/10261/164664
Access Level:acceso abierto
Palabra clave:Conditionals events
Uncertain reasoning
Non-monotonic reasoning
Boolean algebra of conditionals
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spelling On Boolean Algebras of Conditionals and Their Logical CounterpartFlaminio, TommasoGodo, LluisHosni, HykelConditionals eventsUncertain reasoningNon-monotonic reasoningBoolean algebra of conditionalsThis paper sheds a novel light on the longstanding problem of investigating the logic of conditional events. Building on the framework of Boolean algebras of conditionals previously introduced by the authors, we make two main new contributions. First, we fully characterise the atomic structure of these algebras of conditionals. Second, we introduce the logic of Boolean conditionals (LBC) and prove its completeness with respect to the natural semantics induced by the structural properties of the atoms in a conditional algebra as described in the first part. In addition we outline the close connection of LBC with preferential consequence relations, arguably one of the most appreciated systems of non-monotonic reasoning. © Springer International Publishing AG 2017.Flaminio and Godo acknowledge partial support by the Spanish FEDER/MINECO project TIN2015-71799- C2-1-P.Peer ReviewedSpringer NatureMinisterio de Economía y Competitividad (España)European CommissionConsejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]2018201820172018info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Postprintinfo:eu-repo/semantics/acceptedVersionhttp://hdl.handle.net/10261/164664reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Inglés#PLACEHOLDER_PARENT_METADATA_VALUE#MINECO/TIN2015-71799- C2-1-PSíinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/1646642026-05-22T06:33:51Z
dc.title.none.fl_str_mv On Boolean Algebras of Conditionals and Their Logical Counterpart
title On Boolean Algebras of Conditionals and Their Logical Counterpart
spellingShingle On Boolean Algebras of Conditionals and Their Logical Counterpart
Flaminio, Tommaso
Conditionals events
Uncertain reasoning
Non-monotonic reasoning
Boolean algebra of conditionals
title_short On Boolean Algebras of Conditionals and Their Logical Counterpart
title_full On Boolean Algebras of Conditionals and Their Logical Counterpart
title_fullStr On Boolean Algebras of Conditionals and Their Logical Counterpart
title_full_unstemmed On Boolean Algebras of Conditionals and Their Logical Counterpart
title_sort On Boolean Algebras of Conditionals and Their Logical Counterpart
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 Economía y Competitividad (España)
European Commission
Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
dc.subject.none.fl_str_mv Conditionals events
Uncertain reasoning
Non-monotonic reasoning
Boolean algebra of conditionals
topic Conditionals events
Uncertain reasoning
Non-monotonic reasoning
Boolean algebra of conditionals
description This paper sheds a novel light on the longstanding problem of investigating the logic of conditional events. Building on the framework of Boolean algebras of conditionals previously introduced by the authors, we make two main new contributions. First, we fully characterise the atomic structure of these algebras of conditionals. Second, we introduce the logic of Boolean conditionals (LBC) and prove its completeness with respect to the natural semantics induced by the structural properties of the atoms in a conditional algebra as described in the first part. In addition we outline the close connection of LBC with preferential consequence relations, arguably one of the most appreciated systems of non-monotonic reasoning. © Springer International Publishing AG 2017.
publishDate 2017
dc.date.none.fl_str_mv 2017
2018
2018
2018
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/10261/164664
url http://hdl.handle.net/10261/164664
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv #PLACEHOLDER_PARENT_METADATA_VALUE#
MINECO/TIN2015-71799- C2-1-P
Sí
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Springer Nature
publisher.none.fl_str_mv Springer Nature
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
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812455

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