# A Knowledge and Semantic Fusion Method for Automatic Geometry Problem Understanding
## 1 Introduction
To overcome these challenges, this paper introduces three improvements: First, decoupling the ontology and data layers in the knowledge graph and separating the ontology layer into a reusable ontology model, while storing the specific problem's semantic data in the semantic layer. Second, constructing the ontology model as a two-layer architecture, where the upper layer adopts a knowledge-system-type ontology for building a geometry domain knowledge base, and the lower layer employs a semantic-network-type ontology as a bridge between conceptual-level knowledge and object-level text data. Third, the knowledge base is structured around the domain knowledge system, with adjustments for semantic extraction needs to enable knowledge-powered entity relationship extraction. Current GPU methodologies fall into two categories: machine learning (ML)-based and rule/template-based. While ML methods excel in general natural language processing (NLP) tasks, their need for large datasets and computational resources makes them unsuitable for lightweight applications. ML models also suffer from inherent biases, limited interpretability, and difficulties in handling dual-level (text and knowledge) information in resource-constrained scenarios, thus failing to meet GPU's high accuracy requirements. Traditional rule/template methods mainly focus on sentence-level templates, leading to a large number and complexity of templates, with limited semantic coverage and poor flexibility. This paper proposes an innovative knowledge and knowledge-semantic fusion method for Chinese middle-school plane geometry proof problems. The model mimics human problem-understanding cognition by enabling knowledge-guided dual-level information extraction. Specifically, this paper constructs a specialized knowledge base called SGKO, integrating geometry ontology with semantic considerations using knowledge graph technology. With SGKO, the model processes problem text, first performing text-level entity and relation extraction (ERE) using a template-matching-based state machine model IDIM-T, converting unstructured text into structured entities and relationships. Then, the rule-based method IDIM-K conducts knowledge-level ERE, ultimately generating the problem's semantic knowledge graph (abbreviated as 'problem semantic KG'). The key contributions of this study include the following. 1. Global shared dual-layer semantical-enhanced knowledge ontology model (SGKO): By decoupling the ontology layer from the data layer and further constructing the ontology layer as a dual-layer knowledge model for the geometry domain, which consists of an upper-layer geometry domain knowledge and a lower-layer semantic enhancement layer and serves as the common ontology for all problem semantic graphs, this not only resolves the issue of incompatible data granularity in single-layer ontologies for GPU knowledge graphs but also bridges conceptual and object-level information, enabling the integration of problem semantic knowledge graphs with geometry knowledge, but also establishes a geometry domain knowledge model with excellent scalability and maintainability. 2. Dynamically generated modular relationship matching templates and template matching strategies: Starting from atomic relationship units, this paper modularizes and componentizes semantic roles, forming a semantic role framework that records the relative positional information between roles, which consists of argument slots and predicate slots. During relationship extraction, the semantic role framework dynamically assembles into a suitable template framework by querying the knowledge base and, after knowledge injection, is instantiated as usable matching templates. Additionally, by summarizing and categorizing relationship descriptions in problem texts, reusable template matching strategies are designed for different relationship expression types, enabling automatic and dynamic adaptation based on text structure.