Constraint-based Reasoning for Description Logics with Concrete Domains and Aggregations

Aggregation over concrete domains is a very natural extension to Description Logics (DLs), as it allows individuals to be organised by their physical attribute values. However, reasoning support for aggregations, such as sums, counting, or min/ max, has proved challenging, since any naive extension will immediately result in an undecidable logic. This thesis introduces a new DL with concrete domains and aggregations that has useful yet decidable reasoning tasks. It therefore enables the expression of complex phenomena involving numerical values. We show that concept satisfiability for this DL is NP-complete, and describe an implementation based on a sound and complete encoding into Constraint Programming (CP). This enables us to exploit efficient CP solvers that naturally and efficiently deal with both the abstract and concrete parts of the logic at the same time.