Integrating Ontologies and Rules: Semantic and Computational Issues

We present some recent results on the deflnition of logic- based systems integrating ontologies and rules. In particular, we take into account ontologies expressed in Description Logics and rules ex- pressed in Datalog (and its nonmonotonic extensions). We flrst introduce the main issues that arise in the integration of ontologies and rules. In particular, we focus on the following aspects: (i) from the semantic view- point, ontologies are based on open-world semantics, while rules are typ- ically interpreted under closed-world semantics. This semantic discrep- ancy constitutes an important obstacle for the deflnition of a meaningful combination of ontologies and rules; (ii) from the reasoning viewpoint, the interaction between an ontology and a rule component is very hard to handle, and does not preserve decidability and computational proper- ties: e.g., starting from an ontology in which reasoning is decidable and a rule base in which reasoning is decidable, reasoning in the formal sys- tem obtained by integrating the two components may not be a decidable problem. Then, we brie∞y survey the main approaches for the integration of ontologies and rules, with special emphasis on how they deal with the above mentioned issues, and present in detail one of such approaches, i.e., DL+log. Finally, we illustrate the main open problems in this research area, pointing out what still prevents us from the development of both efiective and expressive systems able to integrate ontologies and rules.