Probabilistic Description Logic Programs under Inheritance with Overriding for the Semantic Web

Towards uncertainty reasoning in the Rules, Logic, and Proof layers of the Semantic Web, we present a novel approach to probabilistic description logic programs, which combine probabilistic logic programs, probabilistic default theories, and the description logics behind OWL Lite and OWL DL. The approach is based on new notions of entailment for reasoning with conditional constraints, which realize the principle of inheritance with overriding for both classical and purely probabilistic knowledge. They are obtained by generalizing previous formalisms for probabilistic default reasoning with conditional constraints. In addition to dealing with probabilistic knowledge, the new notions of entailment thus also allow for handling default knowledge. We analyze the semantic properties of the new entailment relations. We also present algorithms for solving the main computational problems related to probabilistic description logic programs under inheritance with overriding.