A Method for Knowledge Representation to Design Intelligent Problems Solver in Mathematics Based on Rela-Ops Model

Abstract

Knowledge-base is a fundamental platform in the architecture of an intelligent system. Relations and operators are popular knowledge in practice knowledge domains. In this paper, we propose a method to represent the model by combining these kinds of knowledge, called the Rela-Ops model. This model includes foundation components consisting of concepts, relations, operators, and inference rules. It is built based on ontology and object-oriented approaches. Besides the structure, each concept of the Rela-Ops model is a class of objects which also have behaviors to solve problems on their own. The processing of algorithms for solving problems on the Rela-Ops model combines the knowledge of relations and operators in the reasoning. Furthermore, we also propose a knowledge model for multiple knowledge domains, in which each sub-domain has the form as the Rela-Ops model. These representation methods have been applied to build knowledge bases of Intelligent Problems Solver (IPS) in mathematics. The knowledge base of 2D-Analytical Geometry in a high-school is built by using the Rela-Ops model, and the knowledge base of Linear Algebra in university is designed by using the model for multiple knowledge domains. The IPS system can automatically solve basic and advanced exercises in respective courses. The reasoning of their solutions is done in a step-by-step approach. It is similar to the solving method by humans. The solutions are also pedagogical and suitable for the learner's level and easy to be used by students studying 2D-Analytical Geometry in high-school and Linear Algebra in university.