Knowledge Representation and Reasoning is at the heart of the great challenge of Artificial Intelligence, especially knowledge-based systems, expert systems and intelligent problem solvers. There have been many models for knowledge such as logics, semantic networks, conceptual graphs, frames and classes. These models are useful tools to design the above systems. However, they are not suitable to represent knowledge in the domains of reality applications. Designing of the knowledge bases and the inference engines of those systems in practice requires representations in the form of ontologies. Ontologies are getting widespread attention as vehicles for sharing concepts within a distributed community, and for modeling domain knowledge. For applications such as the intelligent problem solver in plane geometry, the knowledge contains a complicated system of concepts, relations, operators, functions, and rules. This situation motivates an ontology-based solution with such components. In this article, an ontology, which is called Ontology of Computational Object Knowledge Base (COKB), will be presented in details. We also present a model for representing problems together reasoning algorithms for solving them, and design methods to construct applications. The above methodology has been used in designing some systems for solving problems such as systems for solving analytic geometry problems, solving problems in plane geometry, and the expert system for diabetic micro vascular complication diagnosis.