## 5 Experimental Framework and Results
### Case Study Analysis of CARAG
#### 5.1.3 Smart Prompting for Explanation Generation for Claim 59  
Finally, we independently incorporated the evidence retrieved by each approach, into the LLM prompt to conduct the comparative analysis of explanation generation. This informed prompting (Section 4.3) supports evidence-based fact verification and explanation (post-hoc) generation, leveraging the previously introduced _Llama-2-7b-chat-lif_ model. The LLM prompt for each approach (annotated evidence, RAG, and CARAG) for Claim 59 is formatted as follows:  
* Prompt: <Claim 59 (claim text)> + <K docs> + <specific instruction> (An example for specific instruction is, You are a fact-verification assistant. From the given claim and its evidence, determine if the claim is supported by the evidence and generate a concise explanation (two sentences max))
* <K docs> is the only variable here, which corresponds to the retrieved evidence of each approach (representing the six retrieved evidence items (\(k=6\)) selected for each approach). \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline \multicolumn{2}{c}{**Annotated Evidence**} & \multicolumn{2}{c}{**RAG Retrieved Evidence**} & \multicolumn{2}{c}{**CARAG Retrieved Evidence**} \\ \hline  & 1. & Failure will result in the country’s once-successful car-making industry being scrapped. & 1. \\
1. & Government pledge to act on the climate emergency. & 2. & Two-week journey which would have meant missing Wales’ first match. \\
2. & U.N. notes 1.5 degrees Celsius as a crucial limit. & 3. & Shares fell as low as $6.50-apiecec on Monday, down 97 percent from August 2021. \\
3. & [PERSON]’s opposition to increasing traffic during a climate emergency. & 4. & BMW-branded cars, motorcycles, and Mini models sold since October 1 get the new warranty. & 3. \\
5. & Groundswell NZ’s protest against He Waka Eke Noa. & 5. & Korean officials discussing several possible options to correct what they believe to be unfair policies that eliminated up to $7500 of tax credits for EVs produced outside North America. & 6. \\
6. & White House statement about [PERSON]’s health condition. & & [PERSON]’s health condition. \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of annotated evidence and retrieved evidence through RAG and CARAG, for Claim 59. Specifically, for the annotated evidence approach, <K docs> refers to the items in the 'Annotated Evidence' column of Table 3; and for RAG and CARAG, <K docs> refers to the items in the'RAG Retrieved Evidence' column and 'CARAG Retrieved Evidence' column of Table 3, respectively. Figure 7 presents the generated explanations for each approach, aligned with the three types of prompts. For comprehensiveness, the figure also includes the claim text and its abstractive explanation, providing full context for the claim under investigation. Observations and limitations for each approach are highlighted, offering a thorough view of their respective strengths and constraints. Notably, all three explanations refute the claim, indicating it is not supported by the evidence. The qualitative comparison in Figure 7 further classifies the explanations into local and global reasoning. Explanations based on annotated evidence (left) provide a direct assessment without broader context and are thus categorized as local reasoning. In contrast, the RAG and CARAG explanations, which incorporate a broader set of evidence to provide thematic perspectives beyond the immediate claim, fall under global reasoning. This distinction implies that, despite agreement in claim veracity, each approach offers a unique level of thematic depth. For instance, the RAG-generated explanation addresses broader economic aspects but lacks a direct thematic connection to the climate emergency, resulting in a more surface-level narrative.