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Bayesian Confirmation and Justifications

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Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11726))

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Abstract

We introduce a family of probabilistic justification logics that feature Bayesian confirmations. Our logics include new justification terms representing evidence that make a proposition firm in the sense of making it more probable. We present syntax and semantics of our logic and establish soundness and strong completeness. Moreover, we show how to formalize in our logic the screening-off condition for transitivity of Bayesian confirmations.

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Notes

  1. 1.

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

  2. 2.

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

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Acknowledgements

Hamzeh Mohammadi has been supported by the Ministry of Science, Research and Technology of Iran and part of the research was carried out during a visit at University of Bern.

Thomas Studer has been supported by the Swiss National Science Foundation grant 200021_165549.

Author information

Authors and Affiliations

  1. Department of Mathematical Science, Isfahan University of Technology, Isfahan, Iran

    Hamzeh Mohammadi

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

    Thomas Studer

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  1. Hamzeh Mohammadi
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Correspondence to Thomas Studer .

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Editors and Affiliations

  1. Technische Universität Dortmund, Dortmund, Germany

    Gabriele Kern-Isberner

  2. Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade, Serbia

    Zoran Ognjanović

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Mohammadi, H., Studer, T. (2019). Bayesian Confirmation and Justifications. In: Kern-Isberner, G., Ognjanović, Z. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2019. Lecture Notes in Computer Science(), vol 11726. Springer, Cham. https://doi.org/10.1007/978-3-030-29765-7_34

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  • DOI: https://doi.org/10.1007/978-3-030-29765-7_34

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