Abstract. We extend the description Horn logic DHL [5], which is a fragment of the description logic SHI, to a fragment EDHL of the context-free description logic with inverse roles ALCIcf. We show that the instance checking problem in EDHL has PTime data complexity. Combining EDHL with Datalog we obtain the query language EDHL-Datalog with PTime data complexity. We introduce and study also the general description Horn logic GDHL, which extends EDHL-Datalog by allowing the constructor ∃R.C to appear in the right hand side of terminological inclusion axioms and using definite logic programs instead of Datalog programs. 1

Abstract. It is known that the OWL 2 RL Web Ontology Language Profile has PTime data complexity and can be translated into Datalog. However, a knowledge base in OWL 2 RL may be unsatisfiable. The reason is that, when translated into Datalog, the result may consist of a Datalog program and a set of constraints in the form of negative clauses. In this paper we first identify a maximal fragment of OWL 2 RL called OWL 2 RL + with the property that every knowledge base expressed in this fragment can be translated to a Datalog program and hence is satisfiable. We then propose some extensions of OWL 2 RL and OWL 2 RL + that still have PTime data complexity. 1