# A Knowledge and Semantic Fusion Method for Automatic Geometry Problem Understanding
## 1 Introduction  
In the field of geometry problem understanding (GPU), researchers aim to transform geometry problems expressed in natural language into computer-processable representations, which is essential for tasks such as automated geometry reasoning, problem solving, and diagram drawing, serving as the foundation and key step for geometry mechanization [1, 2, 3]. However, most research focuses on automated reasoning, with lessattention to GPU automation [4]. Furthermore, despite recent advancements, existing studies exhibit limitations in task interpretation and methodological applicability. Current approaches often treat the GPU as an automatic formalization task, identifying geometry elements and relationships to convert them into formal representations. However, these methods are more of a \"knowledge representation translation\" rather than \"text semantic understanding\", missing semantic layers of the problem text. Existing methods simplify entities to geometry elements and relationships to geometry predicates, ignoring crucial components such as numerical values and expressions and missing broader semantic connections. Thus, although these research methods have achieved the goals of GPU to some extent, they are considered overly simplified and lacking a thorough analysis of the requirements of GPU. GPU uniquely intersects geometry domain knowledge and semantic information extraction (SIE). Unlike conventional SIE tasks, GPU deals with dual information levels: text-level (directly mentioned entities and relationships) and knowledge-level (implicit semantic relationships necessary for holistic semantic understanding). For example, understanding that \"D\" in \"D is a point on BC and E is the midpoint of AD\" refer to the same entity is key knowledge-level information that is often overlooked. Figure 1 illustrates three cases where knowledge-level information is overlooked. Ignoring such knowledge-level information results in fragmented and incoherent data. To address this, the introduction of knowledge graph technology is advocated, and GPU is redefined as a knowledge extraction task oriented toward knowledge graphs. The goal is to transform the semantic information of a problem from unstructured text into a structured knowledge graph, using its strong capabilities on knowledge organization, semantic representation and downstream applications. However, knowledge graphs specific to GPU face limitations due to the duality of GPU information, leading to granularity differences in data construction. This paper distinguishes between two types of knowledge graph models: knowledge systems and semantic networks. The former, essentially a knowledge model, represents information as a knowledge category structure (e.g., [5; 6; 7; 8]), meeting GPU's concept-level knowledge needs but not the object-level granularity required for semantic knowledge graphs. The latter, semantic-network-type knowledge graphs (e.g., [9; 10; 11; 12]), focus on relationships between  
Figure 1: Three cases of GPU missing knowledge-level relationships (with red arrows indicating knowledge-level relationships). pieces of information, effectively representing object-level granularity at the text level but failing to link to knowledge-level information. Both types have limitations and cannot simultaneously meet text and knowledge-level needs, posing challenges for knowledge-graph-oriented GPU. Additionally, the integration of geometry and knowledge engineering is insufficient. Unlike fields such as biology and medicine [13; 14], geography [15; 16], and cultural heritage [17], which have relatively complete, publicly available knowledge engineering ontologies, the lack of such frameworks in geometry significantly hinders the application of knowledge graph technology in GPU and the integration of knowledge with intelligent research methods.