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Canonical Extensions of Conditional Probabilities and Compound Conditionals

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Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2022)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1602))

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.

A. Gilio—Retired.

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Acknowledgments

The authors thank the anonymous referees for their comments. 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 funded by MCIN/AEI/10.13039/501100011033. Sanfilippo acknowledges support by the FFR2020-FFR2021 projects of University of Palermo, Italy.

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Authors and Affiliations

  1. IIIA - CSIC, 08193, Bellaterra, Spain

    Tommaso Flaminio & Lluis Godo

  2. Department of SBAI, University of Rome “La Sapienza”, Rome, Italy

    Angelo Gilio

  3. Department of Mathematics and Computer Science, University of Palermo, Palermo, Italy

    Giuseppe Sanfilippo

Authors
  1. Tommaso Flaminio
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  2. Angelo Gilio
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  3. Lluis Godo
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  4. Giuseppe Sanfilippo
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Corresponding author

Correspondence to Giuseppe Sanfilippo .

Editor information

Editors and Affiliations

  1. University of Milano-Bicocca, Milan, Italy

    Davide Ciucci

  2. University of Oviedo, Oviedo, Spain

    Inés Couso

  3. University of Cádiz, Cádiz, Spain

    Jesús Medina

  4. University of Warsaw, Warsaw, Poland

    Dominik Ślęzak

  5. University of Perugia, Perugia, Italy

    Davide Petturiti

  6. Sorbonne Université, Paris, France

    Bernadette Bouchon-Meunier

  7. Iona College, New Rochelle, NY, USA

    Ronald R. Yager

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Flaminio, T., Gilio, A., Godo, L., Sanfilippo, G. (2022). Canonical Extensions of Conditional Probabilities and Compound Conditionals. In: Ciucci, D., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2022. Communications in Computer and Information Science, vol 1602. Springer, Cham. https://doi.org/10.1007/978-3-031-08974-9_47

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  • DOI: https://doi.org/10.1007/978-3-031-08974-9_47

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-08973-2

  • Online ISBN: 978-3-031-08974-9

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