Claudia Schultz Livres

Focusing on the quantifier elimination problem in real closed fields, this work explores its relevance to description logics, particularly in extending systems to handle default concrete domains for non-linear multivariate equations. It includes a comprehensive literature overview of mathematical tools for assessing the satisfiability of non-linear multivariate inequalities. Additionally, the authors briefly discuss practical applications and present a prototype implementation that demonstrates how these concepts are utilized in real-world scenarios.

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.