On Combining Description Logic Ontologies and Nonrecursive Datalog Rules

Reasoning in systems integrating Description Logics (DL) ontologies and Datalog rules is a very hard task, and previous studies have shown undecidability of reasoning in systems integrating (even very simple) DL ontologies with recursive Datalog. However, the results obtained so far constitute a very partial picture of the computational properties of systems combining DL ontologies and Datalog rules. The aim of this paper is to contribute to complete this picture, extending the computational analysis of reasoning in systems integrating ontologies and Datalog rules. More precisely, we first provide a set of decidability and complexity results for reasoning in systems combining ontologies specified in DLs and rules specified in nonrecursive Datalog (and its extensions with inequality and negation): such results identify, from the viewpoint of the expressive abilities of the two formalisms, minimal combinations of Description Logics and Datalog in which reasoning is undecidable. Then, we present new results on the decidability and complexity of the so-called restricted (or safe) integration of DL ontologies and Datalog rules. Our results show that: (1) the unrestricted interaction between DLs and Datalog is computationally very hard even in the absence of recursion in rules; (2) surprisingly, the various ”safeness” restrictions, which have been defined to regain decidability of reasoning in the interaction between DLs and recursive Datalog, appear as necessary restrictions even when rules are not recursive.