  Ontology-mediated query answering (OMQA) is a promising approach to data
access and integration that has been actively studied in the knowledge
representation and database communities for more than a decade. The vast
majority of work on OMQA focuses on conjunctive queries, whereas more
expressive queries that feature counting or other forms of aggregation remain
largely unex-plored. In this paper, we introduce a general form of counting
query, relate it to previous proposals, and study the complexity of answering
such queries in the presence of DL-Lite ontologies. As it follows from existing
work that query answering is intractable and often of high complexity, we
consider some practically relevant restrictions, for which we establish
improved complexity bounds.
