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.