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#### Symbolic Arithmetical Reasoning with Qualified Number Restrictions

##### MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons45140

Ohlbach,  Hans Jürgen
Programming Logics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45401

Schmidt,  Renate A.
Programming Logics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons44660

Programming Logics, MPI for Informatics, Max Planck Society;

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##### Citation

Ohlbach, H. J., Schmidt, R. A., & Hustadt, U. (1995). Symbolic Arithmetical Reasoning with Qualified Number Restrictions. In A. Borgida, M. Lenzerini, D. Nardi, & B. Nebel (Eds.), Proceedings of International Workshop on Description Logics'95 (pp. 89-95). Rome: Dipartimento di Informatica e Sistemistica, Univ. degli studia di Roma.

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.