Finite Query Answering in Expressive Description Logics

Evaluating queries in the presence of background knowledge has been extensively studied in several communities.
In database theory, it is known as query answering under integrity constraints: given a finite database instance and a set of constraints,
determine answers to a query that are certain to hold over any extension of the given instance that satisfies the constraints.
In the knowledge representation community, the database instance and the set of constraints are treated as a single object, called an ontology, but otherwise the problem remains the same, except that different kinds of constraints are interesting. While in database theory constraints are usually very simple, like functionality of relations, or inclusions between relations, in knowledge representation more expressive logics are used. I will focus on so-called description logics (which are a family of extensions of modal logic) and present some recent results obtained with Tomek Gogacz (U Warsaw) and Yazmin Ibanez-Garcia (TU Wien/U Cardiff).