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Probabilities with Gaps and Gluts
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SYSNO ASEP 0543241 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Probabilities with Gaps and Gluts Author(s) Klein, D. (NL)
Majer, Ondrej (UIVT-O) RID, ORCID, SAI
Rad, S. R. (NL)Number of authors 3 Source Title Journal of Philosophical Logic. - : Springer - ISSN 0022-3611
Roč. 50, č. 5 (2021), s. 1107-1141Number of pages 35 s. Publication form Print - P Language eng - English Country NL - Netherlands 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 R&D Projects GA18-00113S GA ČR - Czech Science Foundation (CSF) Method of publishing Open access Institutional support UIVT-O - RVO:67985807 UT WOS 000648081300001 EID SCOPUS 85105538812 DOI 10.1007/s10992-021-09592-x Annotation 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. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2022 Electronic address http://dx.doi.org/10.1007/s10992-021-09592-x
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