This paper proposes an interpretable geometry solution based on the formal language set of text and diagram. Geometry problems are solved using machines; however, machines encounter challenges in natural language processing and computer vision. Significant progress has improved existing methods in the extraction of geometric formal languages. However, the neglect of the graph structure information in the formal language and the lack of further refinement of the extracted language set can lead to poor theorem prediction and poor accuracy in problem solving. In this paper, a formal language graph is constructed using the extracted formal language set and applied to theorem prediction using a graph convolutional network. To better extract the relationship set of diagram elements, an improved diagram parser is proposed. The test results indicate that the improved method has good results when solving interpretable geometry problems.

The long-standing problem of geometric problem solving in artificial intelligence education has attracted widespread attention. It is necessary to combine geometry diagrams and text descriptions to form a logical representation. This involves combining the knowledge of mathematical theorems, generating a solution sequence, and executing to obtain the answer. However, deficiencies in the feature extraction of geometry diagrams and the fusion of diagram text information can lead to poor performance in solving geometry problems. To effectively extract geometry diagram features, this study proposes an improved diagram parser DenseNet, and enhances the semantic representation of cross-modal information by adding auxiliary tasks. A structural and semantic pre-training strategy was used to parse the text description to avoid different problem solving schemes due to subtle differences in the interpretation of text content. Information fusion was realized by connecting the two modal labels, and then the information was sent to the encoder for fusion. The geometric knowledge was generated under the guidance of multi-modal information, and these programs were executed to obtain the results. Additionally, the performance of the proposed geometric neural solution method on the PGPS9K dataset is improved by 1.3% on average. Compared with the Geometry3K dataset, the effectiveness was proven.

This paper proposes an interpretable geometry solution based on the formal language set of text and diagram. Geometry problems are solved by machines, which still poses challenges in natural language processing and computer vision. Significant progress promotes existing methods in the extraction of geometric formal languages. However, the neglect of the graph structure information in the formal language and the lack of further refinement of the extracted language set can lead to the poor effect of the theorem prediction and affect the accuracy in problem solving. In this paper, the formal language graph is constructed by the extracted formal language set and used to theorem prediction by graph convolutional network. So as to better extract the relationship set of diagram elements, an improved diagram parser was proposed. The test results indicate that the improved method has good results in solving the problem with interpretability geometry.