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Abstract

Many inference systems used for concept description logics are
constraint systems that employ tableaux methods.
These have the disadvantage that for reasoning with qualified number
restrictions $n$ new constant symbols are generated for each
concept of the form $(\geq n \ R \ C)$.
In this paper we present an alternative method that avoids the
generation of constants and uses a restricted form of symbolic
arithmetic considerably different from the tableaux method.
The method we use is introduced in
Ohlbach, Schmidt and Hustadt (1995) for reasoning with graded
modalities.
We exploit the exact correspondence between the concept description
language $\cal ALCN$ and the multi-modal version of the
graded modal logic $\overline{\mbox{\bf K}}$ and show how the method
can be applied to $\cal ALCN$ as well.

This paper is a condensed version of Ohlbach et al.\ (1995).
We omit proofs and much of the technical details, but we
include some examples.