# Bayesian Network Model for Learning Arithmetic Concepts
##### Volume 15, Number 3, March 2019, pp. 939-948 DOI: 10.23940/ijpe.19.03.p23.9399481
## Yali Lv^{a,b}, Tong Jing^{a}, Yuhua Qian^{b}, Jiye Liang^{b}, Jianai Wu^{a}, and Junzhong Miao^{a}
^{a}School of Information Management, Shanxi University of Finance and Economics, Taiyuan, 030006, China
^{b}Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education, Shanxi University, Taiyuan, 030006, China
(Submitted on November 14, 2018; Revised on December 15, 2018; Accepted on January 13, 2019)
## Abstract:
An object usually belongs to multiple concepts, but some concepts can be judged directly while other concepts need to be inferred indirectly. To learn some arithmetic concepts from positive integer number sets, we address an arithmetic concept Bayesian network (ACBN) model by taking advantage of Bayesian networks. Specifically, we first give an ACBN model to represent the arithmetic concept knowledge and their direct relationships, and then we design an ACBN model learning algorithm based on domain knowledge. Furthermore, to infer indirectly some arithmetic concepts, we design the learning method of evidence concepts based on the idea of k-nearest neighbors, and then we propose the inference algorithm of the ACBN model. Finally, the experimental results demonstrate that the ACBN model can effectively learn some daily arithmetic concepts.
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