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Logics for Strict Coherence and Carnap-Regular Probability Functions

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Book cover Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations (IPMU 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 854))

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Abstract

In this paper we provide a characterization of strict coherence in terms of the logical consistency of suitably defined formulas in fuzzy-modal logics for probabilistic reasoning. As a direct consequence of our characterization, we also show the decidability for the problem of checking the strict coherence of rational-valued books on classical events. Further, we introduce a fuzzy modal logic that captures Carnap-regular probability functions, that is normalized and finitely additive measures which maps to 0 only the impossible event.

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Notes

  1. 1.

    In the computation we used the fact that \(h=\lnot t\), whence \(1-v(h)=v(\lnot h)=v(t)\).

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Acknowledgments

The author acknowledges partial support by the Spanish Ramon y Cajal research program RYC-2016-19799; the Spanish FEDER/MINECO project TIN2015-71799-C2-1-P and the SYSMICS project (EU H2020-MSCA-RISE-2015 Project 689176).

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Authors and Affiliations

  1. IIIA - CSIC, Campus de la Universidad Autònoma de Barcelona s/n, 08193, Bellaterra, Spain

    Tommaso Flaminio

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  1. Tommaso Flaminio
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Correspondence to Tommaso Flaminio .

Editor information

Editors and Affiliations

  1. Universidad de Cádiz, Cádiz, Cadiz, Spain

    Jesús Medina

  2. Universidad de Málaga, Málaga, Málaga, Spain

    Manuel Ojeda-Aciego

  3. Universidad de Granada, Granada, Spain

    José Luis Verdegay

  4. Universidad de Granada, Granada, Spain

    David A. Pelta

  5. Universidad de Málaga, Málaga, Málaga, Spain

    Inma P. Cabrera

  6. LIP6, Université Pierre et Marie Curie, CNRS, Paris, France

    Bernadette Bouchon-Meunier

  7. Iona College, New Rochelle, New York, USA

    Ronald R. Yager

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Flaminio, T. (2018). Logics for Strict Coherence and Carnap-Regular Probability Functions. In: Medina, J., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations. IPMU 2018. Communications in Computer and Information Science, vol 854. Springer, Cham. https://doi.org/10.1007/978-3-319-91476-3_22

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  • DOI: https://doi.org/10.1007/978-3-319-91476-3_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-91475-6

  • Online ISBN: 978-3-319-91476-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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