Description Logics are currently the most used formalisms for building ontologies, and have been proposed as standard languages for the specification of ontologies in the Semantic Web. The problem of adding rules to Description Logics is currently a hot research topic, due to the interest of Semantic Web applications towards the integration of rule-based systems with ontologies. Most of the approaches in this field concern the study of description logic knowledge bases augmented with rules expressed in Datalog and its nonmonotonic extensions. In this talk we present a set of computational results which identify, from the viewpoint of the expressive abilities of the two formalisms, minimal combinations of Description Logics and (nonmonotonic) Data-log in which reasoning is undecidable. Then, based on the above results, we briefly survey some recent proposals for overcoming such expressive limitations.
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