The use of ontologies in various application domains, such as Data Integration, the Semantic Web, or ontology-based data management, where ontologies provide the access to large amounts of data, is posing challenging requirements w.r.t. a trade-off between expressive power of a DL and efficiency of reasoning. The logics of the DL-Lite family were specifically designed to meet such requirements and optimized w.r.t. the data complexity of answering complex types of queries. In this paper we propose DL-Litebool, an extension of DLLite with full Booleans and number restrictions, and study the complexity of reasoning in DL-Litebool and its significant sub-logics. We obtain our results, together with useful insights into the properties of the studied logics, by a novel reduction to the one-variable fragment of first-order logic. We study the computational complexity of satisfiability and subsumption, and the data complexity of answering positive existential queries (which extend unions...