Efficient Ontology-Mediated Query Answering: : Extending DL-liteR and Linear εLH

The OWL 2 QL profile of the OWL 2 Web Ontology Language, based on the family of description logics called DL-Lite, is designed so that data stored in a standard relational database system (RDBMS) can be queried through an ontology via a rewriting mechanism, i.e., by rewriting the query into an SQL query that is then answered by the RDBMS system, without any changes to the data. In this paper we propose a language whose expressive power goes beyond that of DL-Lite while still allowing query answering via rewriting of queries into unions of conjunctive two-way regular path queries (UC2RPQs) instead of SQL queries. Our language is an extension of both OWL 2 QL and linear epsilon LH: OWL 2 QL is extended by allowing qualified existential quantification on the left-hand side of concept inclusion axioms, and linear epsilon LH by allowing inverses in role inclusion axioms. We identify a syntactic property of the extended language that guarantees UC2RPQ-rewritability. We propose a novel rewriting technique for conjunctive queries (CQs) under our ontology language that makes use of nondeterministic finite state automata. We show that CQ answering in our setting is NLOGSPACE-complete with respect to data complexity and NP-complete for combined complexity; we also show that answering instance queries is NLOGSPACE-complete for data complexity and in PTIME for combined complexity.