Intelligent Problem Solver in Education for Discrete Mathematics

A grand challenge for artificial intelligence in education is building the Intelligent Problem Solver (IPS) for Science Technology Engineering and Math (STEM) Education. The IPS system has to be able to solve the exercises of the course automatically. It has the following criteria: the knowledge base is sufficient, the program can solve the common exercises in the curriculum of the course based on the knowledge base, the solutions are readable, pedagogical and suitable for the learner's level. Discrete Mathematics is an important course for the undergrad technological curriculum at the university. In this course, knowledge about logic and Boolean algebra is the foundation of logical thinking, it helps students improve their skills in logical reasoning, solving the problems. There are many programs for solving problems in propositional logic and first-order logic; nevertheless, they cannot meet the requirements of a learning support system. In this paper, an IPS system in knowledge domain about logic and Boolean algebra has been proposed. This system satisfies the criteria of the STEM education. It helps students to understand the methods for solving basic and advanced problems: simplify the logical expression in propositional logic, reasoning checking, determine the value or the negative expression of of a logical expression in predicate logic, find the minimization expression of a Boolean function with parameter and non-parameter. In this system, the knowledge base about propositional logic, predicate logic and Boolean algebra at the university for undergraduates has been built based on knowledge model of operators. Via this knowledge base, the inference engine has been designed to solve the kinds of general problems in this knowledge domain. The program has been also tested by the students in University of Information Technology, VNU-HCM.