A Knowledge and Semantic Fusion Method for Automatic Geometry Problem Understanding

Geometry problem understanding (GPU) is a fundamental task in machine intelligence for problem-solving, requiring more accurate and complete information extraction than general natural language understanding tasks. This paper proposes a knowledge and semantic fusion method to achieve high-quality, interpretable, and scalable GPU. It extracts text-level and knowledge-level entities and relationships from problem texts and transforms them into a semantic knowledge graph. First, a dual-layer semantic-enhanced knowledge ontology model (SGKO) tailored for the geometry domain is constructed. By separating the ontology and data layers and combining the strengths of both the knowledge system type ontology and the semantic network type ontology, it enables bidirectional association between conceptual-level knowledge and object-level textual data. Second, a dynamically generated modular relationship matching template is introduced, which is decomposed into reusable atomic components and dynamically assembled through knowledge base queries, significantly reducing template quantity while enhancing adaptability to complex text structures. Additionally, a state-machine-based semantic information extraction model (IDIM-T) is designed that achieves efficient and interpretable semantic extraction through categorized relationship description types. This is combined with a rule-based method (IDIM-K) to complete knowledge-level entity relationship extraction. To validate the method, a dataset was constructed from authoritative sources, including past middle school exam questions, textbooks, and exercise books, covering unary, binary, and ternary relationships, as well as single-clause, cross-clause, and multi-relationship conjunction expressions. Experiments on 230 problems with complex relational descriptions showed that the proposed method achieved fully accurate two-level relationship parsing for 91.87% of the problems. Compared with four baseline methods (sentence template-based, Bi-LSTM-based, Transformer-based, and S2-based), the method achieved the highest F1 score (0.974) for 1832 relationships, outperforming the highest F1 score (0.900) of the baselines.