On the SPARQL Direct Semantics Entailment Regime for OWL 2 QL

OWL 2 QL is the profile of OWL 2 targeted to Ontology-Based Data Access (OBDA) scenarios, where large amount of data are to be accessed and thus query answering is required to be especially efficient in the size of such data, namely AC0 in data complexity. On the other hand, the syntax and the semantics of the SPARQL query language for OWL 2 is defined by means of the Direct Semantics Entailment Regime (DSER), which considers queries including any assertion expressible in the language of the queried ontology, i.e., both ABox atoms, TBox atoms and inequalities expressed by means of DifferentIndividuals atoms. Thus, in this paper, we investigate query answering over OWL 2 QL under DSER. In particular, we show that, by virtue of the restricted meaning assigned to existential variables and union, query answering can be reduced to the evaluation of a Datalog program. Finally, we investigate query answering under a new SPARQL entailment regime, called Direct Semantics Answering Regime (DSAR), obtained by modifying DSER in such a way that existentially quantified variables are assigned the classical logical meaning, and provide an algorithm for answering queries over OWL 2 QL ontologies under DSAR, that is AC0 in data complexity, for a class of queries comprising both TBox atoms, ABox atoms and inequalities.