  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.
