Talk: Dominik Klein (Bamberg/Bayreuth), Ondrej Majer (Prag), Soroush Rafiee Rad (Bayreuth)
First degree entailment is a four valued propositional logic, complementing the classical truth values True and False with two non-classical truth values Neither and Both. In an interpretation proposed by Belnap and Dunn, the latter account for possibly incomplete or contradictory information concerning a particular proposition. Recently there have been attempts to expand the logic and its underlying intuition to a probabilistic setting (Dunn & Childers, Majer & Milne). This presentation picks up on the non-classical probability functions defined by Dunn, but redefine the logical connectives in order to avoid some undesirable properties of the original setting. Within the new setting, the presentation also introduces two dynamic operations related to conditionalization and aggregation. First, the talk introduces the necessary ingredients for defining conditional probabilities in a four valued setting. Second, we also present strategies for aggregating four valued probability assignments and show the standard properties for the proposed aggregation procedures.