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On the Algebraic Structure of Conditional Events

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Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9161))

Abstract

This paper initiates an investigation of conditional measures as simple measures on conditional events. As a first step towards this end we investigate the construction of conditional algebras which allow us to distinguish between the logical properties of conditional events and those of the conditional measures which we can be attached to them. This distinction, we argue, helps us clarifying both concepts.

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Notes

  1. 1.

    Among many other references, the reader may get an idea of the arguments in support of Adam’s thesis which sees the probability of a conditional as conditional probability from [2, 10, 11, 19], and from the arguments which reject it as ill-founded from [13, 16].

  2. 2.

    Note that the Rejection Constraint forces us to exclude counterfactual conditionals from our analysis.

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Acknowledgments

The authors are very grateful for the interesting comments by two anonymous reviewers. Flaminio was supported by the Italian project FIRB 2010 (RBFR10DGUA\(_-\)002). Godo acknowledges partial support of the Spanish MINECO project TIN2012-39348-C02-01. Hosni acknowledges the support of the EU Marie Curie IEF-GA-2012-327630 project Rethinking Uncertainty: A Choice-based approach.

Author information

Authors and Affiliations

  1. Dipartimento di Scienze Teoriche e Applicate, Università dell’Insubria, Via Mazzini 5, 21100, Varese, Italy

    Tommaso Flaminio

  2. Artificial Intelligence Research Institute (IIIA - CSIC), Campus de la Univ. Autònoma de Barcelona s/n, 08193, Bellaterra, Spain

    Lluis Godo

  3. London School of Economics, Houghton Street, London, WC2A 2AE, UK

    Hykel Hosni

Authors
  1. Tommaso Flaminio
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  2. Lluis Godo
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  3. Hykel Hosni
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Corresponding authors

Correspondence to Lluis Godo or Hykel Hosni .

Editor information

Editors and Affiliations

  1. Université de Technologie de Compiègne, Compiègne, France

    Sébastien Destercke

  2. Centre de Recherches de Royallieu, Université de Technologie de Compiègne, Compiègne, France

    Thierry Denoeux

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Flaminio, T., Godo, L., Hosni, H. (2015). On the Algebraic Structure of Conditional Events. In: Destercke, S., Denoeux, T. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2015. Lecture Notes in Computer Science(), vol 9161. Springer, Cham. https://doi.org/10.1007/978-3-319-20807-7_10

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  • DOI: https://doi.org/10.1007/978-3-319-20807-7_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-20806-0

  • Online ISBN: 978-3-319-20807-7

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