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Probabilistic Justification Logic

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Logical Foundations of Computer Science (LFCS 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9537))

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Abstract

We present a probabilistic justification logic, \(\mathsf {PPJ} \), to study rational belief, degrees of belief and justifications. We establish soundness and completeness for \(\mathsf {PPJ} \) and show that its satisfiability problem is decidable. In the last part we use \(\mathsf {PPJ} \) to provide a solution to the lottery paradox.

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Notes

  1. 1.

    In order to have a countable language and in order to obtain decidability we restrict our probabilistic operators to the rational numbers.

  2. 2.

    We agree to the convention that the formula \({!^{n-1}} c : {!^{n-2}} c : \cdots : {!c} : c : A\) represents the formula A for \(n=0\).

  3. 3.

    We will usually write \(*_w\) instead of \(*(w)\).

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Acknowledgements

We would like to thank the anonymous referees for many valuable comments that helped us improve the paper substantially.

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Authors and Affiliations

  1. Institute of Computer Science, University of Bern, Bern, Switzerland

    Ioannis Kokkinis & Thomas Studer

  2. Mathematical Institute SANU, Belgrade, Serbia

    Zoran Ognjanović

Authors
  1. Ioannis Kokkinis
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  2. Zoran Ognjanović
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  3. Thomas Studer
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Corresponding author

Correspondence to Thomas Studer .

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Editors and Affiliations

  1. City University of New York , New York, New York, USA

    Sergei Artemov

  2. Cornell University , Ithaca, New York, USA

    Anil Nerode

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Kokkinis, I., Ognjanović, Z., Studer, T. (2016). Probabilistic Justification Logic. In: Artemov, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2016. Lecture Notes in Computer Science(), vol 9537. Springer, Cham. https://doi.org/10.1007/978-3-319-27683-0_13

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  • DOI: https://doi.org/10.1007/978-3-319-27683-0_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27682-3

  • Online ISBN: 978-3-319-27683-0

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