Probabilistic judgment aggregation is concerned with aggregating judgments about probabilities of logically related issues. It takes as input imprecise probabilistic judgments over the issues given by a group of agents and defines rules of aggregating the individual judgments into a collective opinion representative for the group. The process of aggregation can be subject to constraints, i.e., aggregation rules can be required to satisfy certain properties. We explore how probabilistic independence constraints can be represented and incorporated into the aggregation process.

We investigate a probabilistic propositional logic that is an extension of the logic proposed by Fagin et al. [4] with conditional independence formulae. We give an axiomatization which we show to be complete for the kind of inferences allowed by Bayesian networks.