Loopy Propagation in a Probabilistic Description Logic

This paper introduces a probabilistic description logic that adds probabilistic inclusions to the popular logic ALC, and derives inference algorithms for inference in the logic. The probabilistic logic, referred to as CRALC (“credal” ALC), combines the usual acyclicity condition with a Markov condition; in this context, inference is equated with calculation of (bounds on) posterior probability in relational credal/Bayesian networks. As exact inference does not seem scalable due to the presence of quantifiers, we present first-order loopy propagation methods that seem to behave appropriately for non-trivial domain sizes.