XPath for DL Ontologies

Applications of description logics (DLs) such as ontology-based data access (OBDA) require understanding of how to pose database queries over DL knowledge bases. While there have been many studies regarding traditional relational query formalisms such as conjunctive queries and their extensions, little attention has been paid to graph database queries, despite the fact that graph databases have essentially the same structure as knowledge bases. In particular, not much is known about the interplay between DLs and XPath. The latter is a powerful formalism for querying semistructured data: it is in the core of most practical query languages for XML trees, and it is also gaining popularity in theory and practice of graph databases. In this paper we make a step towards coupling knowledge bases and graph databases by studying how to answer powerful XPath-style queries over simple DLs like DL-Lite and EL. We start with adapting the definition of XPath to the DL context, and then proceed to study the complexity of evaluating XPath queries over knowledge bases. Results show that, while query answering is undecidable for the full XPath, by carefully tuning the shape of negation allowed in the queries we can arrive at XPath fragments that have a potential to be used in practice