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A Decidable Multi-agent Logic with Iterations of Upper and Lower Probability Operators

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Foundations of Information and Knowledge Systems (FoIKS 2018)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 10833))

Abstract

We present a propositional logic for reasoning about higher-order upper and lower probabilities. The main technical result is the proof of decidability of the introduced logical system. We also show that the axiomatization for the corresponding logic without iterations of operators, which we developed in our previous work, is also complete for the new class of models presented in this paper.

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Notes

  1. 1.

    For a discussion on higher-order probabilities we refer the reader to [10].

  2. 2.

    The notation is motivated by the logic \(\mathsf {LUPP}\) from [34], where LUP stands for “lower and upper probability”, while the second P indicates that the logic is propositional. We add I to denote iteration of upper and lower operators.

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Acknowledgments

This work was supported by the SNSF project 200021\(\_\)165549 Justifications and non-classical reasoning, by the Serbian Ministry of Education and Science through projects ON174026, III44006 and ON174008, and by ANR-11-LABX-0040-CIMI.

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Authors and Affiliations

  1. Université Paul Sabatier – CNRS, IRIT, 118 Route de Narbonne, 31062, Toulouse CEDEX 9, France

    Dragan Doder

  2. Institute of Computer Science, University of Bern, Neubrueckstrasse 10, 3012, Bern, Switzerland

    Nenad Savić

  3. Mathematical Institute of Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11000, Belgrade, Serbia

    Zoran Ognjanović

Authors
  1. Dragan Doder
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  2. Nenad Savić
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  3. Zoran Ognjanović
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Correspondence to Nenad Savić .

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Editors and Affiliations

  1. Software Competence Center Hagenberg, Hagenberg im Mühlkreis, Austria

    Flavio Ferrarotti

  2. Vienna University of Technology, Vienna, Austria

    Stefan Woltran

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Doder, D., Savić, N., Ognjanović, Z. (2018). A Decidable Multi-agent Logic with Iterations of Upper and Lower Probability Operators. In: Ferrarotti, F., Woltran, S. (eds) Foundations of Information and Knowledge Systems. FoIKS 2018. Lecture Notes in Computer Science(), vol 10833. Springer, Cham. https://doi.org/10.1007/978-3-319-90050-6_10

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  • DOI: https://doi.org/10.1007/978-3-319-90050-6_10

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