Description Logics with Aggregates and Concrete Domains, Part II
Franz Baader, Ulrike Sattler · 1998
We extend dierent 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 satis ability 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.1 Motivation Unlike many other expressive representation formalisms, such as database schema and query languages, basic Description Logic formalisms (e.g., ALC [ Schmidt-Schau & Smolka,1991;Donini et al.,1991 ] ) do not allow for built-in predicates (like comparisons of numbers) and for aggregation functions (like sum, min, max, average, count).The rst de cit was overcome in [ Baader & Hanschke,1991 ] , where a generic extension of ALC by a concrete domain D was proposed.In this extended DL, called ALC(D), abstract individuals (which are described using ALC) can be related to values in the concrete domain D (e.g., the integers, strings, ...) via so-called features, i.e., functional roles.This allows one to describe, for example, managers that spend more money than they earn by Manager u (less(income; expenses)):1