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On Boolean Algebras of Conditionals and Their Logical Counterpart

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Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10369))

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Abstract

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.

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Notes

  1. 1.

    We use the same symbols for connectives in \(\mathcal{L}\) and in \(\mathcal{{CL}}\) without danger of confusion.

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Acknowledgments

We are thankful to the anonymous reviewers. Flaminio and Godo acknowledge partial support by the Spanish FEDER/MINECO project TIN2015-71799-C2-1-P.

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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. Department of Philosophy, University of Milan, Via Festa del Perdono 7, 20122, Milano, Italy

    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 author

Correspondence to Lluis Godo .

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Editors and Affiliations

  1. IDSIA, Lugano, Switzerland

    Alessandro Antonucci

  2. ONERA, Toulouse, France

    Laurence Cholvy

  3. Aix-Marseille University, Marseille, France

    Odile Papini

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Flaminio, T., Godo, L., Hosni, H. (2017). On Boolean Algebras of Conditionals and Their Logical Counterpart. In: Antonucci, A., Cholvy, L., Papini, O. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2017. Lecture Notes in Computer Science(), vol 10369. Springer, Cham. https://doi.org/10.1007/978-3-319-61581-3_23

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  • DOI: https://doi.org/10.1007/978-3-319-61581-3_23

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  • Online ISBN: 978-3-319-61581-3

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