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Probabilities with Gaps and Gluts

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    0543241 - ÚI 2022 RIV NL eng J - Journal Article
    Klein, D. - Majer, Ondrej - Rad, S. R.
    Probabilities with Gaps and Gluts.
    Journal of Philosophical Logic. Roč. 50, č. 5 (2021), s. 1107-1141. ISSN 0022-3611
    R&D Projects: GA ČR(CZ) GA18-00113S
    Institutional support: RVO:67985807
    Keywords : Belnap-Dunn logic * First Degree Entailment * Non-standard probability theory * Probability theory * Bayes’ updating * Jeffrey updating * Probability aggregation
    OECD category: Philosophy, History and Philosophy of science and technology
    Method of publishing: Open access

    Belnap-Dunn logic (BD), sometimes also known as First Degree Entailment, is a four-valued propositional logic that complements the classical truth values of True and False with two non-classical truth values Neither and Both. The latter two are to account for the possibility of the available information being incomplete or providing contradictory evidence. In this paper, we present a probabilistic extension of BD that permits agents to have probabilistic beliefs about the truth and falsity of a proposition. We provide a sound and complete axiomatization for the framework defined and also identify policies for conditionalization and aggregation. Concretely, we introduce four-valued equivalents of Bayes' and Jeffrey updating and also suggest mechanisms for aggregating information from different sources.
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