Canonical Extensions of Conditional Probabilities and Compound Conditionals

In this paper we show 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 con...

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Published inInformation Processing and Management of Uncertainty in Knowledge-Based Systems Vol. 1602; pp. 584 - 597
Main Authors Flaminio, Tommaso, Gilio, Angelo, Godo, Lluis, Sanfilippo, Giuseppe
Format Book Chapter
LanguageEnglish
Published Switzerland Springer International Publishing AG 2022
Springer International Publishing
SeriesCommunications in Computer and Information Science
Subjects
Boolean algebras of conditionals
Conditional probability
Conjunction and disjunction of conditionals
Online AccessGet full text
ISBN9783031089732
3031089731
ISSN1865-0929
1865-0937
DOI10.1007/978-3-031-08974-9_47

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Abstract In this paper we show 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. We do this by first proving that the canonical extension of a full conditional probability on a finite algebra of events to the corresponding algebra of conditionals is compatible with taking subalgebras of events.
AbstractList In this paper we show 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. We do this by first proving that the canonical extension of a full conditional probability on a finite algebra of events to the corresponding algebra of conditionals is compatible with taking subalgebras of events.
Author Godo, Lluis
Sanfilippo, Giuseppe
Gilio, Angelo
Flaminio, Tommaso
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Bouchon-Meunier, Bernadette
Petturiti, Davide
Couso, Inés
Ślęzak, Dominik
Ciucci, Davide
Yager, Ronald R
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Notes A. Gilio—Retired.
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PublicationSubtitle 19th International Conference, IPMU 2022, Milan, Italy, July 11-15, 2022, Proceedings, Part II
PublicationTitle Information Processing and Management of Uncertainty in Knowledge-Based Systems
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Ghosh, Ashish
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Snippet In this paper we show that the probability of conjunctions and disjunctions of conditionals in a recently introduced framework of Boolean algebras of...
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StartPage 584
SubjectTerms Boolean algebras of conditionals
Conditional probability
Conjunction and disjunction of conditionals
Title Canonical Extensions of Conditional Probabilities and Compound Conditionals
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Volume 1602
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