The Data Complexity of Ontology-Mediated Queries with Closed Predicates.

We study the data complexity of ontology-mediated queries in which selected predicates can be closed (OMQCs), carrying out a non-uniform analysis of OMQCs in which the ontology is formulated in one of the lightweight description logics DL-Lite and epsilon L or in the expressive description logic ALCHI. We focus on separating tractable from non-tractable OMQCs. On the level of ontologies, we prove a dichotomy between FO-rewritable and coNP-complete for DL-Lite and between PTime and coNP-complete for epsilon L. We also show that in both cases, the meta problem to decide tractability is in PTime. On the level of OMQCs, we show that there is no dichotomy (unless NP equals PTime) if both concept and role names can be closed. For the case where only concept names can be closed, we tightly link the complexity of OMQC evaluation to the complexity of generalized surjective CSPs. We also identify a useful syntactic class of OMQCs based on DL-Lite(R) that are guaranteed to be FO-rewritable.