Semantics and inference for Probabilistic Description Logics

We present a semantics for Probabilistic Description Logics that is based on the distribution semantics for Probabilistic Logic Programming. The semantics, called DISPONTE, allows to express assertional probabilistic statements. We also present two systems for computing the probability of queries to probabilistic knowledge bases: BUNDLE and TRILL. BUNDLE is based on the Pellet reasoner while TRILL exploits the declarative Prolog language. Both algorithms compute a propositional Boolean formula that represents the set of explanations to the query. BUNDLE builds a formula in Disjunctive Normal Form in which each disjunct corresponds to an explanation while TRILL computes a general Boolean pinpointing formula using the techniques proposed by Baader and Peñaloza. Both algorithms then build a Binary Decision Diagram (BDD) representing the formula and compute the probability from the BDD using a dynamic programming algorithm. We also present experiments comparing the performance of BUNDLE and TRILL.