Expressive queries over light-weight ontologies

Light-weight Description Logics, such as DLLite, found their applications in practical tasks like Ontology Based Data Access and OWL 2 entailment regimes. These applications require solving not only classical logical problems, like satisfiability and entailment, but also answering database-style queries over knowledge bases. The theory of conjunctive query answering in this setting is now relatively comprehencive. But the real-world applications require a possibility to pose more complex queries over ontologies. In this talk I describe the state of the art in query answering of extensions of conjunctive queries when posed over knowledge bases, such as aggregate queries, queries with different forms of negation and graph-databases style queries.