| The application of artificial intelligence in the field of education,the realization of intelligent answers to mathematical problems by computers,and the creation of mathematical reasoning systems have always been hot issues in the field of automatic reasoning.In the 1950 s,scholars began to study the realization of mechanical proofs of geometric theo-rems.Later,some institutions and scholars also tried to design some expert systems based on knowledge bases,reasoning engines,or pattern matching to achieve intelligent solutions to mathematical problems.In recent years,machine learning technology has also been applied to the research of mathematical reasoning systems.With the rapid development of artificial intelligence technology,the field of automatic reasoning continues to innovate.At the same time,the rapid development of knowledge graph technology and deep learning technology has significant advantages in knowledge reasoning.They have been used in many fields such as medicine and ecommerce,and have achieved many good results.Therefore,the purpose of this thesis is to apply the knowledge graph and deep learning technology to the scientific research project ”Elementary Math Problem Solving System” so that the system can realize deep graph reasoning for solving elementary mathematical problems.The main contributions include the following three parts:(1)Construction of elementary mathematics knowledge graphAn accurate and comprehensive industry knowledge graph is the foundation of the reasoning system.Primary school mathematics usually refers to the knowledge of mathematics at the primary and secondary levels.Considering that the main purpose of the problemsolving system is to take the ”college entrance examination”,this thesis com-piles ”People’s Education Edition” and ”Beijing Normal University Edition” based on the elementary mathematics knowledge points in junior high school and senior high school textbooks.As supplementary material for mainstream teaching,a knowledge graph of elementary mathematical concepts has been established,including 551 entities,561 relationships,and 204763 triples.The knowledge graph is stored by the graph database Neo4 j,and a corresponding knowledge base project written in JAVA language is established to manage it.(2)Deep graph embedding technology based on Deep WalkThe graph network structure of the mathematical knowledge graph is reconstructed,the relationship of the knowledge graph is modeled to be nodes,and the walking strategy and sampling method of the algorithm model is improved on the basis of the Deep Walk algorithm.Finally,a knowledge representation model has been established,which can be better applied to the elementary mathematical knowledge graph and suitable for the task,and the representation vector of mathematical entities and mathematical relationships in the knowledge graph is obtained.(3)Application of deep learning in the graph reasoning systemThe reasoning of the graph reasoning system depends on the matching of the problem knowledge graph and the rule instance knowledge graph.In this thesis,the graph embedding is applied to the vector representation of the problem and rule knowledge graph,and the vector cosine distance is used as the prediction rule of the graph reasoning system.Based on the examples,the graph match system is optimized,the matching order of rule instance knowledge graph is sorted.In addition,a geometric theorem knowledge graph and a geometric theorem sequence conversion module are implemented,and multiple serialized geometric theorem models are trained based on the language model GPT-2,and the proof sequence is filtered through the designed evaluation function,thereby improving proof the theorem.The ability to prove geometric problem solving ability in graph reasoning system. |
