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Revision with unchanged content. This work investigates the quantifier elimination problem in real closed fields with respect to the application in description logics. The motivation for the investigation in this topic is mainly based on the demand for an extension of description logic systems to support a default concrete domain for non-linear multivariate equations and inequations. The authors provide a literature overview that summarizes main mathematical tools for checking whether a set of non-linear multivariate (in-)equatins is satisfiable (quantifier elimination problem). The authors shortly describe how application examples are handled with a prototype implementation.

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Dr. Ralf Moeller is Professor for Computer Science at the Hamburg University of Technology (TUHH) since 2003. In 1996, he received the degree Dr. rer. nat. from the University of Hamburg. Claudia Schultz, Master of Science, Dipl.-Phys., Dipl.-Inform. Claudia Schultz, Master of Science, Dipl.-Phys., Dipl.-Inform.

Claudia Schultz, Master of Science, Dipl.-Phys., Dipl.-Inform.: Studies of Computer Science at Bowling Green State University, Studies of Physics and Computer Science at Universit t Hamburg. Software-Engineer and IT-Consultant at T-Systems GEI GmbH, Hamburg. Analyselead at Otto (GmbH & Co KG), Hamburg.

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