Complexity of answering counting aggregate queries over DL-LiteDL-Lite

The ontology based data access model assumes that users access data by means of an ontology, which is often described in terms of description logics. As a consequence, languages for managing ontologies now need algorithms not only to decide standard reasoning problems, but also to answer database-like queries. However, fundamental database aggregate queries, such as the ones using functions COUNT and COUNT DISTINCT, have received very little attention in this context, and even defining appropriate semantics for their answers over ontologies appears to be a non-trivial task. Our goal is to study the problem of answering database queries with aggregation in the context of ontologies. This paper presents an intuitive semantics for answering counting queries, followed by a comparison with similar approaches that have been taken in different database contexts. Afterwards, it exhibits a thorough study of the computational complexity of evaluating counting queries conforming to this semantics.Our results show that answering such queries over ontologies is decidable, but generally intractable. However, our semantics promotes awareness on the information that can be obtained by querying ontologies and raises the need to look for suitable approximations or heuristics in order to allow efficient evaluation of this widely used class of queries.