A Mathematical Approach for Representing Knowledge about Relations and Its Application

Knowledge-based system is an important component in intelligent systems. Nowadays, there are many knowledge models that have been proposed and applied. However, these methods are not efficient for both executing and using in practical applications. Instead, mathematical approach is an effective method for representing knowledge formally, and this method can be applied to specify real knowledge domains. Besides, knowledge about relations is a popular form of human´s knowledge. In this paper, we will present a mathematical approach for representing knowledge about relations. This knowledge model includes concepts, relations and inference rules of knowledge domain. On this model, the algorithms which solve the problems are designed and proved to be effective. Moreover, this knowledge model has been applied to build a knowledge-based system of plane geometry. In specific, a system for automatic solving problems in plane geometry has been designed.