Query Rewriting For Ontology-Mediated Conditional Answers

Among many solutions for extracting useful answers from incomplete data, ontology-mediated queries (OMQs) use domain knowledge to infer missing facts. We propose an extension of OMQs that allows us to make certain assumptions-for example, about parts of the data that may be unavailable at query time, or costly to query-and retrieve conditional answers, that is, tuples that become certain query answers when the assumptions hold. We show that querying in this powerful formalism often has no higher worst-case complexity than in plain OMQs, and that these queries are first-order rewritable for DL-Lite(R). Rewritability is preserved even if we allow some use of closed predicates to combine the (partial) closed- and open-world assumptions. This is remarkable, as closed predicates are a very useful extension of OMQs, but they usually make query answering intractable in data complexity, even in very restricted settings.