# A Knowledge and Semantic Fusion Method for Automatic Geometry Problem Understanding
## 2 Related Work
### Rule/Template-Based Methods  
Rule/template-based methods extract entities and relationships through predefined pattern-matching rules, offering high precision and interpretability. Inter-GPS uses regular expression-based rule matching to convert problem text into symbolic logic expressions [46]; GeoDRL follows a similar approach to build its semantic parser for formalizing problem texts [47]. GeometryNet identifies geometry entities using POS tagging and rule-based methods [48]. [PERSON] et al. introduced a geometric knowledge ontology that combines pattern-matching algorithms to extract relationships from geometric propositions [49]. [PERSON] et al. [50] and [PERSON] et al. [51] established sentence-level matching templates for recognizing relationships in problem text. Despite the high accuracy of this kind of method, their design logic leads to three significant challenges: First, independent templates are needed for each linguistic variant of the same relationship (e.g., \"AB\(\parallel\)CD\", \"CD is parallel to AB\", and \"AB and CD are parallel\" require separate templates). Second, for multi-relationship descriptions (e.g., \"Point M lies on the perpendicular bisector CG of BD, and GE intersects AC and DM at points P and Q\"), not only is it necessary to think about combinations of atomic relationships, but also the handling of entity sharing and nested structures, leading to exponential growth in template numbers. Third, relationships spanning multiple clauses (e.g., \"In \(\triangle ABC\),..., altitude AD...\") often go undetected. [PERSON] et al. proposed the S2 model [52; 53; 54], simplifying matching objects into relationship keywords, entity types, and quantities to optimize traditional templates. Specifically, the method first uses NLP tools (ICTCLAS) for word segmentation, POS tagging, and sentence boundary detection. Then, it uses a classification-based entity recognition approach to extract geometry elements and relationship words. Third, the S2 model matches relationship words and element types to generate formalized atomic propositions. The S2 model has been applied in many studies for text relationship extraction. For example, [PERSON] et al. used the S2 model to understand texts related to solid geometry calculation problems [55]. [PERSON] et al. used the S2 model to extract explicit relationships from circuit problems in secondary physics and proposed a unit-theorem-based method to handle implicit relationships [56], while [PERSON] et al. applied the S2 model to arithmetic word problems to handle explicit relationships [57]. Some studies have improved the S2 model. For example, [PERSON] et al. expanded the S2 model pool to recognize more types of relationships [58]. [PERSON] et al. proposed a relaxed syntax-semantics method to optimize the original study's limitation of matching only one S2 model per paragraph [59]. [PERSON] et al. improved the original text-based matching mechanism by proposing a vectorized-S2 (VM-S2) model based on BERT to extract quantity relationships from arithmetic word problems [60], and [PERSON] et al. used VM-S2 to extract basic geometry relationships from algebraic problems [61]. Although the S2 model effectively solves the first issue in traditional methods, the latter two still remain unresolved. While the relaxed-S2 method permits repeated calls to the S2 model, this does not fully resolve the relationship combination issue. Additionally, this method faces problems in capturing semantic roles, which leads to relationship extraction errors. For instance, failing to distinguish between \"AB is the perpendicular bisector of CD\" and \"AB's perpendicular bisector is CD\" results in logical direction errors that affect the accuracy of relationship extraction. To address these issues, this paper proposes a new method that starts from limited atomic relationship units and decouples semantic roles and records their relative positional information to form a freely combinable Relationship Semantic Role Framework (RSF).