Artificial intelligence based systems are known for conveying knowledge through machines. This knowledge is often represented using logic representation languages. One of the well-known families of such languages is called Description Logic (DL) which formally reasons and represents knowledge on the concepts, roles and individuals of an application domain. DL reasoners have been evolving and upgraded through the years, however when it comes to handling more complicated ontologies with big values occurring in number restrictions, the current reasoners mostly fail to perform efficiently. One of the techniques used in DL reasoners is the so-called atomic decomposition technique which combines arithmetic and logical reasoning. This thesis presents a customized CPLEX-based solver for enhancing DL reasoners through optimizing the atomic decomposition technique. Furthermore, we provide evidence on how this method can improve the reasoning performance by optimizing atomic decomposition. For such purpose, an empirical evaluation of our system for a set of synthesized benchmarks is demonstrated
