## 3 Materials and Methods
### Question Answering Method
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Datasets** & **TabFact** & **WikiTQ** & \multicolumn{2}{c}{**FeTaQA**} \\ \hline
**Metric** & **acc** & **acc** & **BLEU** & **ROUGE-1** \\ \hline \multicolumn{5}{c}{Generic Reasoning} \\ \hline gpt-3.5-16k-0613 0-shot & 70.45 & 51.84 & 27.67 & 0.61 \\ gpt-3.5-16k-0613 2-shot & 71.24 & 52.32 & - & - \\ gpt-3.5-16k-0613 4-shot & 71.54 & 52.56 & - & - \\ Text-to-SQL gpt-3.5 & 64.71 & 52.90 & - & - \\ Dater LLaMA2-13b & 65.12 & 41.44 & 29.37 & 0.63 \\ Chain-of-Thought gpt-3.5 & 65.37 & 52.48 & - & - \\ \hline \multicolumn{5}{c}{SLM Reasoning} \\ \hline Qwen2-7b Zero-Shot & 60.21 & 45.84 & - & - \\ Llama3-8b Zero-Shot & 61.34 & 46.78 & - & - \\ \hline \multicolumn{5}{c}{TQAgentMethods} \\ \hline Qwen2-7b+TQAgent & 64.43 & 46.23 & - & - \\ Qwen2-7b-Instruct+TQAgent & 68.42 & 49.72 & - & - \\ Llama3-8b+TQAgent & 69.71 & 48.81 & 27.47 & 0.61 \\ Llama3-8b-Instruct+TQAgent & 73.60 & 52.94 & 28.62 & 0.61 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of table question answering. BLEU score increases from 27.47 to 28.62, indicating improved semantic alignment between generated answers and reference texts. Notably, the unchanged ROUGE-1 score suggests that knowledge injection primarily optimizes semantic reasoning rather than lexical overlap. These results validate that knowledge graphs mitigate LLM hallucinations by providing structured world knowledge and constrained reasoning paths, particularly for cross-domain commonsense reasoning and implicit relationship inference in tabular data. The synergy between dynamic operation trees and knowledge retrieval mechanisms enables multi-dimensional table analysis while maintaining lightweight model deployment. **Case Study**

In the case of verifying whether the statement \"the wildcasts kept the opposing team scoreless in four games\" is true, multiple steps are involved. The key information is extracted through the step-by-step processing of the table, and finally, the authenticity of the statement is confirmed. As shown in Figure 3, this case demonstrates how to use basic atomic operations such as row selection, column selection, and group statistics to process complex table data into a form convenient for verifying the statement. The process starts from the original table containing game information. First, specific rows (rows 2, 3, 5, and 9) are selected according to the instruction. Then, the \"opponent\" and \"opponents\" columns are selected from the obtained sub-table. Next, grouping statistics are performed according to the \"opponents\" column. Finally, based on the grouping results, it is determined that the statement \"The wildcasts kept the opposing team scoreless in 3 games\" is true, and the answer \"YES\" is given. In the case shown in Figure 4, the process of KG injection is demonstrated. After the initial table operations are performed, the system identifies the need for additional contextual information--specifically, the country to which each city belongs. To address this, the model executes a _kg_inject_ action, triggering a self-reflection mechanism powered by the LLM. During this self-reflection, the model identifies that the table lacks the country information necessary for a more comprehensive analysis. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Datasets** & **TabFact** & **WikiTQ** & \multicolumn{2}{c}{**FeTaQA**} \\ \hline
**Metric** & **acc** & **acc** & **BLEU** & **ROUGE-1** \\ \hline \(n=1\) & 64.43 & 46.23 & 26.32 & 0.55 \\ \(n=2\) & 66.25 & 47.98 & 27.15 & 0.57 \\ \(n=3\) & 69.22 & 50.78 & 28.21 & 0.60 \\ \(n=4\) & 73.54 & 52.89 & 28.58 & 0.61 \\ \(n=5\) & 73.59 & 52.90 & 28.61 & 0.61 \\ \(n=6\) & 73.60 & 52.94 & 28.62 & 0.61 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Impact of sampling values.