Probabilities with Gaps and Gluts

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
http://dx.doi.org/10.1007/s10992-021-09592-x

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.
Permanent Link: http://hdl.handle.net/11104/0320492