## 4 Experiment
### Case Studies  
This section provides the following two cases. In order to better analyze the advantages and disadvantages of DaGATN in the logical reasoning MRC task, we selected two cases from the verification set for the case study.  
Case 1 comes from MF type logical reasoning, and the reasoning process of DaGATN is shown in Figure 6:  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multirow{2}{*}{**Dev (\%)**} & \multicolumn{2}{c}{**ReClor**} & \multicolumn{2}{c}{**LogiQA**} \\  & & **Test (\%)** & **Test-E (\%)** & **Test-H (\%)** & **Dev** & **Test** \\ \hline DeBERTa-xlarge & 72.60 & 71.00 & 83.41 & 61.25 & 44.40 & 41.50 \\ \hline +DGCN w/o PosEmbed & 76.00 & 72.19 & 83.80 & 63.10 & 43.62 & 42.71 \\ +DGAT w/o PosEmbed & 74.20 & 73.40 & 84.09 & 65.00 & 44.90 & 44.25 \\ +DGCN, PosEmbed & 76.30 & 72.54 & 83.61 & 61.90 & 43.40 & 43.20 \\ DaGATN & 74.60 & 74.30 & 85.22 & 65.71 & 44.71 & 44.50 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Overview of the results from the ablation experiments.  
As can be seen, for the context and candidate answers, DaGATN's modeling of the reasoning process makes the model well recovered from the human thinking pattern when citing one answer to another. The flawed pattern of reasoning in context is that the protagonist claims that his opinion is confirmed, while the confirmation comes from a group that has nothing to do with that opinion. First, DaGATN extracts 6 EDUs based on relation connectives and punctuations for each branch, and among them five pairs of discourse relationships are detected. For argument branch, there are two referential relations (EDU1-EDU2, EDU4-EDU5) and for punctuation branch there are three implicit relations (EDU2-EDU3, EDU3-EDU4, EDU5-EDU6). The topology of the two graphs provides an explicit understanding of the text. Additionally, we display the attention maps from the final layer of the graph attention network for both branches, as well as the overall attention map after merging according to the strategy (blue for the argument branch, red for the punctuation branch, and purple for the merged). The data in the attention matrices is mapped to the range of \([0,1]\) for a clearer illustration. The darker the color, the stronger the correlation between two logical units. These weighted attention maps effectively showcase the relationships and offer a broader perspective for interpretability. Through the argument graph, the model understands that this pattern of flaws requires the protagonist to claim that a point of view is confirmed. Afterwards, through the punctuation graph, the model understands that the view is shared by practitioners in unrelated domains. Finally, the model selects the correct option D from the options based on this feature.  
Although the overall performance of DaGATN is better than other models, there is still potential for improvement on some specific types of logical inference problems. After analyzing the test results, we found that the model performs uncompetitively on MS and ER type problems due to the lack of modeling for the logical symbolic aspect. And our model performs poorly on IF type problems, which require an understanding of the more abstract conceptual deficiencies of error arguments, and DaGATN falls short in this regard.  
Case 2 comes from MF type logical reasoning, and the reasoning process of DaGATN is shown in Figure 7:  
Figure 6: Illustration of reasoning process of case 1.  
As can be seen, based on the context, DaGATN disentangles two reasoning processes for the flawed viewpoint, the first focusing on \"All sides of all Stories\", and the second focusing on \"All sides of important stories\". The model's modeling of the reasoning processes led it to focus more on the explicit differences between the two reasoning outcomes and to select option C based on this feature, ignoring the fact that it was viewed as a whole and categorized as a type of error. For this example, option A is the correct answer.