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Nowadays, designing knowledge-based systems which involve knowledge from different domains requires deep research of methods and techniques for knowledge integration, and ontology integration has become the foundation for many recent knowledge integration methods. To meet the requirements of real-world applications, methods of ontology integration need to be studied and developed. In this paper, an ontology model used as the knowledge kernel is presented, consisting of concepts, relationships between concepts, and inference rules. Additionally, this kernel is also added to other knowledge, such as knowledge of operators and functions, to form an integrated knowledge-based system. The mechanism of this integration method works upon the integration of the knowledge components in the ontology structure. Besides this, problems and the reasoning method to solve them on the integrated knowledge domain are also studied. Many related problems in the integrated knowledge domain and the reasoning method for solving them are also studied. Such an integrated model can represent the real-world knowledge domain about operators and functions with high accuracy and effectiveness. The ontology model can also be applied to build knowledge bases for intelligent problem solvers (IPS) in many mathematical courses in college, such as linear algebra and graph theory. These IPSs have great potential in helping students perform better in those college courses.

A Method of Ontology Integration for Designing Intelligent Problem Solvers