The increasing popularity of the Semantic Web has lead to a wide-spread adoption of Description Logics (DLs) for modeling real world domains. Given the nature of such domains and the origin of the available data, the capability of managing probabilistic and uncertain information is of foremost importance. As a result, the last decade has seen an exponential increase in the interest for the development of methods for combining probability with DLs.

This tutorial will present various probabilistic semantics for knowledge bases (KBs). The tutorial will then concentrate on one of them, DISPONTE, which is inspired by the distribution semantics of Probabilistic Logic Programming. The tutorial will also describe approaches and algorithms to reason upon probabilistic knowledge bases. An overview of the major systems will be provided and three reasoners and two learning algorithms for the DISPONTE semantics will be presented more in details. BUNDLE and TRILL are able to find explanations for queries and compute their probability w.r.t. DISPONTE KBs while TRILL^{P} compactly represents explanations using a Boolean formula and computes as well the probability of queries. The system EDGE learns the parameters of axioms of DISPONTE KBs while LEAP learns both the structure and parameters of KBs.

TRILL and TRILL^{P} can be tested online at http://trill.ml.unife.it