# A Knowledge and Semantic Fusion Method for Automatic Geometry Problem Understanding
## 5 Information Detect and Interpret Model
### Text-Level ERE and IDIM-T
#### 5.1.1 Relationship Mention Types  
This paper classifies the types of relationship mentions in geometry problem descriptions to facilitate targeted relationship extraction. **Definition 8** (Relationship Description). : _A relationship description refers to any textual representation of a relationship, i.e., a textual instantiation of a relationship. Denote a relationship description as rd._  
The relationship description of a binary relationship is called a binary relationship description. Let \(RD_{Binary}\) represent the set of relationship descriptions for a binary relationship \(r_{binary}\). For all \(rd_{binary}\in RD_{Binary}\), it contains a \(kw\in KW_{Autonomous}\), as well as mentions of \(e_{subject}\) and \(e_{object}\). A \(rd_{binary}\) constitutes a complete relationship mention. A relationship description of a ternary relationship is called a ternary relationship description. The set of relationship descriptions for a ternary relationship \(r_{ternary}\) can be represented as \(RD_{Ternary}=(RD_{Core}\times RD_{Attached})\cup RD_{Core}\). For all \(rd_{core}\in RD_{Core}\), it is the relationship description of its \(r_{core}\), containing a \(kw_{core}\) and mentions of \(e_{subject}\) and \(e_{object}\); for all \(rd_{attached}\in RD_{Attached}\), it is a relationship description of \(r_{attached}\), containing a \(kw_{attached}\) and a mention of \(e_{additional}\). A ternary relationship description \(rd_{ternary}\in RD_{Ternary}\) can be described in two ways: with and without mentioning \(rd_{attached}\). For example, for a binary relationship where AB is parallel to CD, both \"AB\(\parallel\)CD\" and \"CD is parallel to AB\" are its relationship descriptions, and they are both binary relationship descriptions. Similarly, for a ternary relationship where AB is perpendicular to CD with the foot at P, both \"AB\(\perp\)CD at P\" and \"AB is perpendicular to CD, P is the foot of the perpendicular\" are its complete relationship descriptions that with \(rd_{attached}\), while \"AB\(\perp\)CD\" is a relationship description that does not mention \(rd_{attached}\). **Definition 9** (Relationship Mention). : _A relationship mention refers to a text segment that mentions a relationship. A relationship can be mentioned in the text in any way (individually, concurrently, or otherwise), whether the mentioned relationship is complete or incomplete. All relationship descriptions fall under a type of relationship mention._  
\begin{table} \begin{tabular}{l l l} \hline
**Method** & **Extension Effort** & **Potential Impact** \\ \hline Rule/Template-Based & Design rules/templates for & May introduce template \\ Methods & atomic and composite & conflicts \\ \hline Machine Learning & New corpus collection, & May impact accuracy of \\ Methods & model retraining/ & other entity/relationship \\  & fine-tuning (, annotation) * & extraction \\ \hline Proposed Method &
\begin{tabular}{l} Configure three kinds of \\ knowledge attributes \\ \end{tabular} & Zero interference \\ \hline \end{tabular}   
The difference between a relationship description and a relationship mention is that the former starts with a specific relationship, while the latter is based on the perspective of the text. For example, \"the foot is E\" would not be considered a complete relationship description because it is not a complete relationship, but it is a way of mentioning a relationship. Similarly, \"point M, N are the midpoints of AC and EF, respectively\" is a way of mentioning a relationship and consists of two relationship descriptions. Geometry problem texts are segmented into clauses C using commas or periods. Each clause \(c\in C\) is treated as a potential relationship mention. The clauses are categorized into a four-quadrant framework based on the count and completeness of relationships within single or multiple clauses.