MathCLM: Mathematical Cognitive Learning Model Based on the Evolution of Knowledge Graph.

In real-world applications, the effective integration of learning and reasoning in a cognitive agent model is a challenging mission. However, such integration may lead to a better understanding, practice, and construction of more realistic models, especially for mathematical learning. Unfortunately, existing models are either oversimplified or require much processing time, which is unsuitable for online learning and education. Therefore, we propose a novel cognitive learning model, called Mathematical Cognitive Learning Model (MathCLM) based on the evolution of knowledge graph, for online mathematical learning that seeks to effectively represent, learn, and reason in online learning environments. The model's architecture combines cognitive learning with symbolic knowledge representation based on natural language processing (NLP). We introduce the mathematical instance concept to build the strategies by mathematical knowledge, such as theorems, axioms, etc., and infer new custom instances based on the learning knowledge. Furthermore, it can deal with uncertainty and errors from instances recommendation using a graph matching model and displays the inference progressing with different combinations of instances. We build a platform to promote and validate our model. The validation of the model on the real-world platform and the results presented here indicate the promise of the approach when performing online learning and reasoning in real-world scenarios, with possible applications in various areas.