Tableau reasoning for description logics and its extension to probabilities

The increasing popularity of the Semantic Web drove to a widespread adoption of Description Logics (DLs) for modeling real world domains. To help the diffusion of DLs, a large number of reasoning algorithms have been developed. Usually these algorithms are implemented in procedural languages such as Java or C++. Most of the reasoners exploit the tableau algorithm which features non-determinism, that is not easily handled by those languages. Prolog directly manages non-determinism, thus is a good candidate for dealing with the tableau’s non-deterministic expansion rules. We present TRILL, for “Tableau Reasoner for descrIption Logics in proLog”, that implements a tableau algorithm and is able to return explanations for queries and their corresponding probability, and TRILLP, for “TRILL powered by Pinpointing formulas”, which is able to compute a Boolean formula representing the set of explanations for a query. Reasoning on real world domains also requires the capability of managing probabilistic and uncertain information. We show how TRILL and TRILLP can be used to compute the probability of queries to knowledge bases following DISPONTE semantics. Experiments comparing these with other systems show the feasibility of the approach.