Canonical Extensions of Conditional Probabilities and Compound Conditionals

• Published in: Information 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
• Language: English
• Published: Switzerland Springer International Publishing AG 2022; Springer International Publishing
• Series: Communications in Computer and Information Science
• Subjects: Boolean algebras of conditionals; Conditional probability; Conjunction and disjunction of conditionals
• ISBN: 9783031089732; 3031089731
• ISSN: 1865-0929; 1865-0937
• DOI: 10.1007/978-3-031-08974-9_47

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.