# A Knowledge and Semantic Fusion Method for Automatic Geometry Problem Understanding
## 5 Information Detect and Interpret Model
### Text-Level ERE and IDIM-T
#### 5.1.3 Relationship Extraction  
This subsection outlines the modules involved in relationship extraction and describes the basic and specific processes within them. The relationship extraction process begins by taking a clause \(c\) and processing it keyword by keyword, outputting intermediate results including sets of relationship triplets \(R_{c}\) and entity sets \(E_{c}\). \begin{table}
\begin{tabular}{l l} \hline
**RMT** & **Identification Basis** \\ \hline \multirow{4}{*}{SC-B} & (1) \(c\) contains one \(kw_{autonomous}\) and no \(kw_{attached}\). \\  & (2) For \(ktv_{autonomous}\in KW_{rt}\), there is \(rt\in RT_{Binary}\). \\  & (3) All argument entities (subject and object) are in \(c\), and each argument slot mentions only one entity. \\ \hline \multirow{4}{*}{SC-T} & (1) \(c\) contains one \(kw_{autonomous}\) and one \(kw_{attached}\). \\  & (2) \(kw_{autonomous},kw_{attached}\in KW_{rt}\), and \(rt\in RT_{Ternary}\). \\  & (3) All argument entities, and additional entity are in \(c\), and each argument slot mentions only one entity. \\ \hline \multirow{4}{*}{SI-B} & (1) \(c\) contains \(kw_{autonomous}\in KW_{rt}\) with \(rt\in RT_{Binary}\). \\  & (2) There is a missing argument in \(c\), usually the subject entity. \\  & (3) The missing argument entity is usually in a clause before the current \(c\), and its entity type usually belongs to the polygon class. \\ \hline \multirow{4}{*}{SI-T} & (1) The complete relationship description involves two consecutive clauses \(c_{i}\) and \(c_{i+1}\), i is the index of the clause in \(C\). \\  & (2) In the case of Attached relationship separation: \(rd_{core}\) is in \(c_{i}\), \(rd_{attached}\) is in \(c_{i+1}\). \\  & \(kw_{core}\) is in \(c\). \(c_{i+1}\) contains only one \(kw_{attached}\), which is the relationship description of \(r_{attached}\) in that clause. There are only \(kw_{attached}\) and additional entity in that clause. \\  & (3) In the case of Subject entity separation, \(kw_{core}\) is in \(c_{i+1}\), subject entity is in \(c_{i}\). \\ \hline \multirow{4}{*}{MC-S} & (1) \(c\) contains more than one \(kw_{autonomous}\). \\  & (2) Let \(KW_{c}\) be the set of all autonomous keywords in \(c\). For the relationships involving the current \(kw\in KW_{c}\), all its arguments are in \(c\). \\  & (3) There is one or more entities in the same argument slot. Multiple entities are connected by conjunctions (such as \",\" (ideographic comma), \"and\", etc.). \\ \cline{1-1}  & (4) The possible correspondences in the number of entity mentions between argument slots include three types: 1-to-1 (e.g., “AB intersects CE at point E”), 1-to-m (e.g., “AB respectively intersects CE, DF at points P, Q”, “AE, BF intersect CD at P, Q”), and m-to-m situations (e.g., “Points E, F respectively are the midpoints of AC, BC”). \\ \cline{1-1}  & (5) For m-to-m, entities belonging to the same relationship have the same index in all argument slot mentions. \\ \hline \multirow{4}{*}{MC-D} & (1) \(c\) contains more than one \(kw_{autonomous}\). \\  & (2) For the relationships involving the current \(kw\in KW_{c}\), all its arguments are in \(c\). \\ \cline{1-1}  & (3) \(c\) is linguistically termed as a multi-predicate sentence structure where all relationship descriptions share the same sentence subject. \\ \hline \multirow{4}{*}{MT} & (1) \(c\) contains more than one \(kw_{autonomous}\). \\ \cline{1-1}  & (2) \(c\) contains complete relationship descriptions and at least one incomplete relationship description. \\ \cline{1-1}  & (3) In the cases of Attached Relationship Isolation and Subject Entity Isolation, the whole relationship description belongs to the current type. \\ \hline \end{tabular}
\end{table} 
Table 5: Identification criteria for RMTs. 1. Processing Modules  
The relationship extraction process involves the following five modules: Knowledge Linking, Relationship Detection, Relationship Matching Template Generation, Relationship Extraction, and Relationship Structured Representation Generation.