Method for solving problems on a knowledge model of operators

Knowledge models play a very important role for designing knowledge base systems. There are many effective methods for representing such as: rule-based system, computational network, ontology. In fact, a popular form of knowledge domain is knowledge about operations and computational relations, especially in building the intelligent problem solver for computational knowledge domain about mathematics and physic. The intelligent problem solver must have sufficient knowledge to solve problems automatically, and their solutions are natural, step-by-step and can be understand by the learners. However, these current methods are not effective for representation practical application. In this paper, we present an mathematical approach for building knowledge model of operator. This model represents knowledge about the operators between objects. It includes three components: concepts, operators, and inference rules. Based on this model, the method for solving some problems about operators is studied, such as: Reducing an expression, Prove an equality of expressions. Moreover, this model has been applied to specify a part of knowledge domain about Vector Algebra and construct a program for solving some problems on this knowledge domain.