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.
Highlights
Science Technology Engineering and Math (STEM) is a modern approach for studying in the technological era [3]
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 results of our system and Symbolab for solving problems in [33] are shown in Table 5 and Fig. 5: The knowledge base of Symbolab is designed as frames, so it only can solve the kinds of exercises that had been set up, especially it cannot solve exercises in a section about vector spaces
Summary
Science Technology Engineering and Math (STEM) is a modern approach for studying in the technological era [3]. The Rela-Ops model satisfies the criteria of a method for representing the knowledge base of IPS in education. We present a method to represent a knowledge domain, including multiple sub-domains; each sub-domain has the Rela-Ops model form These proposed methods have been applied to build knowledge bases of IPS in mathematics. RELATED WORK Nowadays, there are many methods for representing knowledge, including formal logic, frames, networks, ontology, and algebraic approaches They have some limitations to apply in practice, especially in designing knowledge bases of IPS in education. STRUCTURE OF RELA-OPS MODEL Rela-Ops model is a model for representing the combining knowledge of relations and operators It is built based on ontology and object-oriented approach, in which an object in this model has behaviors to solve problems on its own. We only mention the model and solving methods for general problems
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