Solving problems on a knowledge model of operators and application

Knowledge of operators is useful to build the intelligent problem solver for knowledge domains about computing. In this paper, we present a mathematical approach for building a knowledge model of operators, called Ops-model. The foundation of this model includes: concepts, operators, and inference rules. Each concept of this model is a class of objects with the behaviours for solving problems on themselves. General problems on this model are also studied, such as: reducing an expression, prove an equality of expressions. The algorithms for solving these problems are also designed. Ops-model has been applied to specify a part of knowledge domain about vector algebra in high school. It is used to construct a program for solving some problems on this knowledge domain. The solutions of this program are step-by-step, readable and suitable with the learners' level. It is useful for supporting students to learn this subject.