Description Logics with Aggregates and Concrete Domains, Part II

We extend different Description Logics by concrete domains (such as integers and reals) and by aggregation functions over these domains (such as min,max,count,sum), which are usually available in database systems. We present decision procedures for the inference problems satisfiability for these Logics-provided that the concrete domain is not too expressive. An example of such a concrete domain is the set of (nonnegative) integers with comparisons (=,≤, ≤n, ...) and the aggregation functions min, max, count.This is a new, extended version of a report with the same number. An abridged version has appeared in the Proceedings of the European Conference on Artificial Intelligence, Brighton, UK, 1998