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European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty

ECSQARU 2017: Symbolic and Quantitative Approaches to Reasoning with Uncertainty pp 491–500Cite as

A First-Order Logic for Reasoning About Higher-Order Upper and Lower Probabilities

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

Abstract

We present a first-order probabilistic logic for reasoning about the uncertainty of events modeled by sets of probability measures. In our language, we have formulas that essentially say that “according to agent Ag, for all x, formula \(\alpha (x)\) holds with the lower probability at least \(\frac{1}{3}\)”. Also, the language is powerful enough to allow reasoning about higher order upper and lower probabilities. We provide corresponding Kripke-style semantics, axiomatize the logic and prove that the axiomatization is sound and strongly complete (every satisfiable set of formulas is consistent).

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Notes

  1. 1.

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

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Acknowledgments

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

Author information

Authors and Affiliations

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

    Nenad Savić

  2. Faculty of Mechanical Engineering, Belgrade, Serbia

    Dragan Doder

  3. Mathematical Institute of SASA, Belgrade, Serbia

    Zoran Ognjanović

Authors
  1. Nenad Savić
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  2. Dragan Doder
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  3. Zoran Ognjanović
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Corresponding author

Correspondence to Nenad Savić .

Editor information

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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Savić, N., Doder, D., Ognjanović, Z. (2017). A First-Order Logic for Reasoning About Higher-Order Upper and Lower Probabilities. 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_44

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  • DOI: https://doi.org/10.1007/978-3-319-61581-3_44

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-61580-6

  • Online ISBN: 978-3-319-61581-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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