Counterfactual-Consistency Prompting for Relative Temporal Understanding in Large Language Models
Authors: Jongho Kim, seung-won hwang
Accepted at: acl25

Counterfactual-Consistency Prompting for Relative Temporal Understanding in Large Language Models

Jongho Kim and Seung-won Hwang*
Interdisciplinary Program in Artificial Intelligence, Seoul National University
{jongh97, seungwonh}@snu.ac.kr

Abstract
Despite the advanced capabilities of large language models (LLMs), their temporal reasoning ability remains underdeveloped. Prior works have highlighted this limitation, particularly in maintaining temporal consistency when understanding events. For example, models often confuse mutually exclusive temporal relations like “before” and “after” between events and make inconsistent predictions. In this work, we tackle the issue of temporal inconsistency in LLMs by proposing a novel counterfactual prompting approach. Our method generates counterfactual questions and enforces collective constraints, enhancing the model’s consistency. We evaluate our method on multiple datasets, demonstrating significant improvements in event ordering for explicit and implicit events and temporal commonsense understanding by effectively addressing temporal inconsistencies.

1 Introduction
Despite the impressive capabilities of LLMs, a line of research (Jain et al., 2023; Chu et al., 2023) has highlighted that these models often lack temporal reasoning abilities. This is especially true for relative event understanding, where the goal is to infer temporal relationships between events or properties within an event in the passage, without depending on absolute time indicators (e.g., specific dates).

The primary challenge is that LLMs lack temporal consistency in their responses (Qiu et al., 2024; Chen et al., 2024). Temporal consistency is defined as the model’s ability to ensure that conflicting timelines do not co-exist. For instance in Figure 1-(a), if the model is temporally inconsistent, mutually exclusive temporal relations like “before” and “after” are sometimes confused when ordering events, leading to contradictory predictions—such as stating that Event A happens both before and after Event B in the same context.

![Example of leveraging counterfactual questions to resolve temporal inconsistency in LLMs.](page_682_355_682_312.png)

Figure 1: Example of leveraging counterfactual questions to resolve temporal inconsistency in LLMs.

While events with time indicators are often addressed with mathematical reasoning (Zhu et al., 2023; Su et al., 2024), no existing work has successfully tackled the challenge of temporal inconsistency in the events’ relative understanding without requiring explicit time markers. Chain-of-thought (CoT) reasoning (Wei et al., 2022), which primarily aids mathematical and symbolic reasoning (Sprague et al., 2024), is also reported to fail to solve such inconsistency (Qiu et al., 2024). Considering temporal consistency is fundamental in temporal reasoning, its absence in LLM can undermine key tasks like planning (Sakaguchi et al., 2021; Zhang et al., 2024). These observations highlight the need for alternative reasoning skills to achieve temporal consistency.

This study answers the following research question: Can we prompt LLMs to elicit the ability to mitigate temporal inconsistency? Inspired by counterfactual augmentation, where models are exposed with lexically similar, but typically label-
flipping pairs in training (Kaushik et al., 2020), we extend it to LLMs to generate temporally counterfactual questions: We introduce lexically small interventions to the original input (e.g. before to after, years to centuries) that drastically affect its temporal semantics. By providing these questions and self-generated answers alongside the original input, the model would rely less on lexical similarities and better understand the semantics.

To this end, we propose a novel counterfactual-consistency prompting (CCP), designed to enhance the temporal consistency of LLMs, as described in Figure 1-(b). CCP first generates temporal counterfactual exemplars and then applies the insights gained to address the original temporal question. This method is particularly effective in relative event understanding because the counterfactual exemplars not only encourage the model to understand different temporal semantics but also directly impose temporal constraints. For instance, if the model states that “Event A happens after Event B” and also recognizes that “Event A happens before Event B”, the conflict forces the model to collectively re-weight the validity of these two statements.

We show performance gain of CCP across multiple relative event understanding tasks. Our effectiveness in mitigating temporal inconsistencies is further demonstrated by our inconsistency metric.

2 Method

Our idea is to make the model approximate the temporal constraints using counterfactuals. Because temporal reasoning imposes unique interdependencies, where one temporal aspect affects another (Han et al., 2019; Kim et al., 2024), counterfactuals enable us to capture these constraints. For example, if the model establishes from a counterfactual exemplar that “Event e_1 happens [r_2: before] Event e_2”, it is constrained to predict the original question that “Event e_1 cannot happen [r_1: after] Event e_2”:

\[
r_2(e_1, e_2) \in \mathcal{V} \implies r_1(e_1, e_2) \not\in \mathcal{V}
\]

where \( r(e_a, e_b) \) represents the temporal relation \( r \) between events \( e_a \) and \( e_b \), and \( \mathcal{V} \) represents the set of coherent temporal relations with the context.

2.1 Generating Temporally Counterfactual Questions

Given a context \( C \), our task is to provide an accurate answer to question \( Q \) while maintaining temporal consistency. We start by creating temporally counterfactual questions, \( Q^{c_1}...Q^{c_i} \).

Counterfactual augmentation conventionally aims to generate instances with lexically minimal edits while keeping others unchanged (Huang et al., 2019; Kaushik et al., 2020; Wang and Culotta, 2020). This strategy discourages models from relying too much on superficial similarity. However, previous works (Kaushik et al., 2020) require arbitrary label-flipping edits, which are unsuitable for LLM inference with unknown test labels.

In contrast, we focus on temporally counterfactual questions that specifically edit the temporal semantics of the original sentence. Our approach ensures that the model adheres to the “temporal constraints”, yet retains the effect of label-flipping that emphasizes temporal cues over superficial similarity.

Specifically, we set the types of counterfactual questions based on the temporal semantics each dataset aims to capture. The types of temporal counterfactuals are listed in Table 1. For sentences representing temporal relation between two events (\( r_1(e_1, e_2) \)), we substitute the relation \( r_1 \) to \( r_2 \), or event \( e_2 \) to \( e_3 \). For those representing an event’s temporal properties (\( r_1(e_1) \)) such as duration or stationarity, we substitute the property to \( r_2 \) or negate it to \( \neg r_1 \).

To generate counterfactual questions, we design our model to dynamically create them rather than rely on a predefined rule-based template. While rule-based approaches like Chen et al. (2024) in logical reasoning constrain answers using a predefined question set, they limit flexibility to cover the broad range of temporal expressions. By comparison, our dynamic generation of constraints provides a more adaptable solution. We specify various counterfactual types through in-context learning (ICL) to control the relevance of these generated questions. The full prompts are in Appendix F.1.

2.2 Counterfactual-Consistency Prompting

After generating the counterfactual questions, we prompt the model again to produce predictions for counterfactual \( Y^{c_1}, ..., Y^{c_n} \). However, there is a risk when LLMs may fail to answer the counterfactual questions correctly. In this case, their direct use propagates errors to the original question.

As a proxy for determining whether the generated prediction can be trusted, existing works aggregate multiple predictions of the same ques-
<table>
  <tr>
    <th>Dataset</th>
    <th>Relation</th>
    <th>Revision Type</th>
    <th>Example</th>
  </tr>
  <tr>
    <td>TempEvalBi-QA</td>
    <td>\( r_1(e_1, e_2) \)<br>\( r_2(e_1, e_2) \)</td>
    <td>Original<br>\( r_1 \rightarrow r_2 \)</td>
    <td>Did they get married <b>after</b> they moved to Maine?<br>Did they get married <b>before</b> they moved to Maine?</td>
  </tr>
  <tr>
    <td>TRACIE</td>
    <td>\( r_1(e_1, e_2) \)<br>\( r_2(e_1, e_2) \)</td>
    <td>Original<br>\( r_1 \rightarrow r_2 \)</td>
    <td>Chad found the cap <b>before</b> he got off of the ride.<br>Chad found the cap <b>after</b> he got off of the ride.</td>
  </tr>
  <tr>
    <td>MCTACO: Duration</td>
    <td>\( r_1(e_1) \)<br>\( r_2(e_1) \)</td>
    <td>Original<br>\( r_1 \rightarrow r_2 \)</td>
    <td>It has existed for <b>1 year</b>.<br>It has existed for <b>centuries</b>.</td>
  </tr>
  <tr>
    <td>MCTACO: Frequency</td>
    <td>\( r_1(e_1) \)<br>\( r_2(e_1) \)</td>
    <td>Original<br>\( r_1 \rightarrow r_2 \)</td>
    <td>It rained a <b>couple of times</b> in the summer.<br>It rained <b>every month</b> in the summer.</td>
  </tr>
  <tr>
    <td>MCTACO: Stationarity</td>
    <td>\( r_1(e_1) \)<br>\( r_2(e_1) \)</td>
    <td>Original<br>\( r_1 \rightarrow r_2 \)</td>
    <td>She is <b>still</b> in Ranchipur.<br>She is <b>not</b> in Ranchipur.</td>
  </tr>
  <tr>
    <td>MCTACO: Ordering</td>
    <td>\( r_1(e_1, e_2) \)<br>\( r_1(e_1, e_3) \)</td>
    <td>Original<br>\( e_2 \rightarrow e_3 \)</td>
    <td>They <b>went to the store</b> after they were put in jail.<br>They <b>repented</b> after they were put in jail.</td>
  </tr>
  <tr>
    <td>MCTACO: Typical Time</td>
    <td>\( r_1(e_1) \)<br>\( r_2(e_1) \)</td>
    <td>Original<br>\( r_1 \rightarrow r_2 \)</td>
    <td>Durer died <b>40 years</b> later.<br>Durer died <b>360 years</b> later.</td>
  </tr>
</table>

Table 1: The temporal aspects targeted by each dataset and types of counterfactuals addressed by our framework. The examples illustrate how counterfactual questions modify the semantics regarding temporal relations (\( r_1, r_2 \)) for events (\( e_1, e_2, e_3 \)).

tion (Wang et al., 2023; Du et al., 2024). Formally, the refined prediction \( Y \) is derived by re-weighting the probability distribution \( P \) of previous predictions \( Y_1, ..., Y_n \) from the same question as: \( P(Y) = f(P(Y_1), ..., P(Y_n)) \) where \( f \) is an aggregation function such as majority voting or LLM itself. Though, they can lead to errors as they solely rely on feedback from a single question.

Our distinction is to aggregate predictions from both the original and counterfactual questions. We design the model to re-weight the counterfactual answer distributions across the questions.

\[
P(Y) = f(P(Q, Y), P(Q^{c_1}, Y^{c_1}), ..., P(Q^{c_n}, Y^{c_n}))
\]

For instance, even if the model wrongly predicts the relation as ‘after’ in a counterfactual, collectively considering the possibility of the relation ‘before’ can re-weight the effect of the constraint. The prompts are provided in Appendix F.2.

This re-evaluation approach improves robustness against potential errors in generated answers. The second analysis in Subsection 3.5 shows such self-correction outperforms a baseline directly leveraging counterfactuals without aggregation.

3 Experiments

3.1 Datasets

Among publicly available datasets, we selected three based on two criteria: (1) the task focuses on relative event understanding without absolute time indicators, and (2) the temporal inconsistency on the dataset can be evaluated.

TempEvalQA-Bi (Qiu et al., 2024) involves ordering two explicit events in time, assessing temporal consistency in mutually exclusive question pairs. TRACIE (Zhou et al., 2021) expands the event ordering to implicit events, testing if the hypothesis logically follows the story. We finally added MCTACO (Zhou et al., 2019) considering the diverse event-related temporal properties. The dataset covers broader aspects like event duration or frequency. We modified the multiple-choice setting of MCTACO into a binary question-answering task for consistency evaluation, presenting each answer candidate separately to determine if it fits the context. Dataset statistics and examples are in Appendix A.

3.2 Metrics

Along with accuracy (ACC) and F1 scores to assess overall performance, we introduce the inconsistency metric (INC) as a main evaluation measure for temporal inconsistency. We define the INC as the percentage of inconsistent predictions. An inconsistency is counted when at least one incorrect answer is found within a group of minimally dissimilar questions with slight modifications in their temporal semantics, while all other aspects remain unchanged.

TempEvalQA-Bi directly provides this metric. For TRACIE, we manually group questions that are counterfactual to each other. We adapt INC in MCTACO by grouping original multiple-choice candidates by question.

3.3 Evaluation Settings and Baselines

For models, we used open-source LLM Llama-3 8B and 70B (AI@Meta, 2024), and API-based LLM GPT-4o-mini and GPT-4o (OpenAI et al.,
<table>
  <tr>
    <th rowspan="2"></th>
    <th colspan="3">TempevalQA-Bi</th>
    <th colspan="3">TRACIE</th>
    <th colspan="3">MCTACO</th>
  </tr>
  <tr>
    <th>ACC</th><th>F1</th><th>INC (↓)</th>
    <th>ACC</th><th>F1</th><th>INC (↓)</th>
    <th>ACC</th><th>F1</th><th>INC (↓)</th>
  </tr>
  <tr>
    <td>Llama -3-8B</td>
    <td>SP</td><td>65.4</td><td>63</td><td>57.6</td>
    <td>57.4</td><td>66.9</td><td>75.2</td>
    <td>77.7</td><td>69.4</td><td>59.8</td>
  </tr>
  <tr>
    <td></td>
    <td>CoT</td><td>69.6</td><td>70.6</td><td>50</td>
    <td>63</td><td>64.9</td><td>56</td>
    <td>77.6</td><td>69.8</td><td>63.4</td>
  </tr>
  <tr>
    <td></td>
    <td>Consistency</td><td>70.8</td><td>71.2</td><td>49.6</td>
    <td>64.9</td><td>67.3</td><td>57.8</td>
    <td>77.5</td><td>69.0</td><td>61.1</td>
  </tr>
  <tr>
    <td></td>
    <td>Reflection</td><td>63.6</td><td>63.9</td><td>44.6</td>
    <td>62.5</td><td>55.7</td><td>55.5</td>
    <td>77.4</td><td>69.7</td><td>76.4</td>
  </tr>
  <tr>
    <td></td>
    <td>Debate</td><td>67.6</td><td>65.2</td><td>52.2</td>
    <td>63.6</td><td>66</td><td>53.2</td>
    <td>37.4</td><td>31.6</td><td>88.1</td>
  </tr>
  <tr>
    <td></td>
    <td>CCP</td><td><b>75.9</b></td><td><b>75.2</b></td><td><b>32.7</b></td>
    <td><b>68.8</b></td><td><b>70.4</b></td><td><b>39.8</b></td>
    <td><b>78.7</b></td><td><b>81.7</b></td><td><b>57.7</b></td>
  </tr>
  <tr>
    <td>Llama -3-70B</td>
    <td>SP</td><td>76.6</td><td>78.6</td><td>39.7</td>
    <td>79.9</td><td>79.7</td><td>29.6</td>
    <td>85.2</td><td>81.8</td><td>43.5</td>
  </tr>
  <tr>
    <td></td>
    <td>CoT</td><td>80.4</td><td>82</td><td>31.3</td>
    <td>80.1</td><td>80</td><td>31.8</td>
    <td>85.9</td><td>82.2</td><td>46.9</td>
  </tr>
  <tr>
    <td></td>
    <td>Consistency</td><td>-</td><td>-</td><td>-</td>
    <td>-</td><td>-</td><td>-</td>
    <td>-</td><td>-</td><td>-</td>
  </tr>
  <tr>
    <td></td>
    <td>Reflection</td><td>77</td><td>77.9</td><td>35.3</td>
    <td>80</td><td>78.3</td><td>30.3</td>
    <td>80.6</td><td>73</td><td>56.5</td>
  </tr>
  <tr>
    <td></td>
    <td>Debate</td><td>81</td><td>82.8</td><td>32.6</td>
    <td>81.6</td><td>80.7</td><td>25.9</td>
    <td>85.3</td><td>81.4</td><td>45.9</td>
  </tr>
  <tr>
    <td></td>
    <td>CCP</td><td><b>87.3</b></td><td><b>87.9</b></td><td><b>19.2</b></td>
    <td><b>86.5</b></td><td><b>86.1</b></td><td><b>12.0</b></td>
    <td><b>89.4</b></td><td><b>87.6</b></td><td><b>37.0</b></td>
  </tr>
  <tr>
    <td>GPT-4o-mini</td>
    <td>SP</td><td>78.8</td><td>76.4</td><td>36.6</td>
    <td>74.6</td><td>71.3</td><td>38.2</td>
    <td>76.0</td><td>63.1</td><td>65.8</td>
  </tr>
  <tr>
    <td></td>
    <td>CoT</td><td>81.3</td><td>79.9</td><td>29</td>
    <td>73.2</td><td>68.5</td><td>42.7</td>
    <td>80.9</td><td>73.7</td><td>58.9</td>
  </tr>
  <tr>
    <td></td>
    <td>Consistency</td><td>85.5</td><td>85.5</td><td>21.9</td>
    <td>73.6</td><td>68.8</td><td>42.8</td>
    <td>78.9</td><td>69.4</td><td>60.6</td>
  </tr>
  <tr>
    <td></td>
    <td>Reflection</td><td>86.8</td><td>86.9</td><td>22.8</td>
    <td>74.4</td><td>70.9</td><td>39.1</td>
    <td>74.8</td><td>60.2</td><td>68.5</td>
  </tr>
  <tr>
    <td></td>
    <td>Debate</td><td>86.4</td><td>86.4</td><td>24.6</td>
    <td>73</td><td>67.1</td><td>44.5</td>
    <td>78.3</td><td>68.2</td><td>61.0</td>
  </tr>
  <tr>
    <td></td>
    <td>CCP</td><td><b>88.8</b></td><td><b>88.7</b></td><td><b>19.6</b></td>
    <td><b>82.5</b></td><td><b>81.2</b></td><td><b>20.2</b></td>
    <td><b>87.8</b></td><td><b>85.8</b></td><td><b>42.1</b></td>
  </tr>
  <tr>
    <td>GPT-4o</td>
    <td>SP</td><td>86.4</td><td>85.8</td><td>20.1</td>
    <td>80.1</td><td>78.6</td><td>27.0</td>
    <td>79.7</td><td>70.9</td><td>60.5</td>
  </tr>
  <tr>
    <td></td>
    <td>CoT</td><td>90.4</td><td>90</td><td>17.4</td>
    <td>80.2</td><td>78.1</td><td>32.4</td>
    <td>84.4</td><td>80</td><td>49.7</td>
  </tr>
  <tr>
    <td></td>
    <td>Consistency</td><td>91.7</td><td>91.5</td><td>14.7</td>
    <td>80.1</td><td>77.7</td><td>31.4</td>
    <td>82.9</td><td>77.3</td><td>49.7</td>
  </tr>
  <tr>
    <td></td>
    <td>Reflection</td><td>93.1</td><td>93</td><td>11.2</td>
    <td>82.7</td><td>80.9</td><td>26.6</td>
    <td>80.0</td><td>72.2</td><td>55.4</td>
  </tr>
  <tr>
    <td></td>
    <td>Debate</td><td>90.8</td><td>90.6</td><td>11.2</td>
    <td>80.6</td><td>77.9</td><td>32.8</td>
    <td>81.4</td><td>74.6</td><td>52.2</td>
  </tr>
  <tr>
    <td></td>
    <td>CCP</td><td><b>93.8</b></td><td><b>93.8</b></td><td><b>8.0</b></td>
    <td><b>85.8</b></td><td><b>84.7</b></td><td><b>17.6</b></td>
    <td><b>90.4</b></td><td><b>88.8</b></td><td><b>35.0</b></td>
  </tr>
</table>

Table 2: The full performance comparison results on the relative event understanding tasks. Our prompting methods, which leverage self-generated exemplars as the temporal constraint, outperform baselines across the board.

2024).

For baselines, we first compare CCP with standard prompting (SP) that directly answers the question without intermediate steps, and CoT, which incorporates step-by-step reasoning to derive the answer. Next, we consider methods that aggregate multiple predictions of the same question. Self-Consistency (Wang et al., 2023) predicts one question multiple times and performs majority voting. Self-Reflect methods (Madaan et al., 2024; Shinn et al., 2024) iteratively refine own predictions. Multi-agent Debate (Du et al., 2024) leverages both majority vote and reflection. We employ a 3-shot setting across all configurations. More details on evaluation settings are in Appendix B.

3.4 Main results

Table 2 highlights the performance of our method compared to baseline methods on relative event understanding tasks. Compared to SP, the CoT baseline is not usually effective and often worsens performance. Advanced baselines, Consistency, Reflect, and Debate, also fail to consistently reduce inconsistencies or achieve competitive accuracy. In contrast, CCP steadily outperforms these baselines across various LLMs, significantly reducing temporal inconsistencies across all datasets and achieving notable improvements in ACC and F1 scores.

3.5 Analysis

Creating counterfactual questions by generation handles diverse temporal aspects. We compared our generative setting with the Retrieved Questions (Ret.Q) approach, where counterfactual questions were retrieved from other questions within the same question group. We evaluated the methods on MCTACO, which covers various aspects of event reasoning.

Figure 2 shows that generating counterfactual questions proved more effective for all temporal
types. These results suggest that our method performs better in event understanding with diverse relations, where the dataset cannot often provide high-quality counterfactual questions. Notably, CCP outperforms the Ret.Q baseline even though our method may produce incorrect questions. Also, CCP is more practical since Ret.Q assumes the questions in the test set are observed.

![Bar chart comparing INC (%) between Ret.Q and CCP across different metrics: Overall, Event Ordering, Event Duration, Frequency, Stationarity, Typical Time](page_312_370_486_246.png)

Figure 2: Comparison between counterfactual example collection methods on MCTACO with Llama-3-8B.

![Bar chart comparing INC (%) between Dir.A and CCP on TempEvalQA-Bi and TRACIE](page_312_654_486_246.png)

Figure 3: Comparison between different counterfactual leveraging methods with the Llama-3-8B model.

CCP is robust against wrong counterfactual exemplars. We conducted a comparative analysis of two methods: Direct Answering (Dir.A), which involves answering directly from counterfactual exemplars, versus CCP which leverages the aggregation step to re-evaluate them. We conducted experiments on TempEvalQA-Bi and TRACIE, where before-after relations ensure that identifying a counterfactual answer is sufficient to determine the original. We excluded MCTACO since its counterfactual answers do not always determine the validity of the original answer. In the Dir.A implementation, the answer to the counterfactual question is flipped and directly used as the response to the original question. The results in Figure 3 demonstrate that CCP consistently outperforms Dir.A, supporting our robustness by the collective evaluation.

CCP’s performance gain is orthogonal to the number of ICL examples. Our approach inevitably introduces additional counterfactual examples during in-context learning (ICL), leading to a higher total number of shots compared to the baseline. To ensure a more competitive baseline, we increased the total number of shots in the baseline. In the MCTACO dataset and with the Llama model, we additionally experimented with the 12-shot CoT, which includes 12 passage (P)-question (Q)-candidate (C) pairs, and compared them with our 3-shot. We note that our 3-shot examples include 3 passage-question pairs and 11 candidates.

The results in Table 3 demonstrate that our method significantly outperforms the CoT, even with the increased number of examples in the baseline (INC score: 60.0 for CoT vs. 57.7 for Ours). This indicates that the performance gains are not simply due to the inclusion of more examples but are primarily driven by leveraging temporal constraints through counterfactual questions to enhance reasoning.

Additionally, we tested whether our approach benefits from additional ICL examples. The results in the last row of Table 3 confirm this, showing an improvement in INC score from 57.7 to 49.8, further validating the potential performance gain of our method.

<table>
  <tr>
    <th rowspan="2"></th>
    <th colspan="4">MCTACO</th>
  </tr>
  <tr>
    <th>#P-Q</th>
    <th>#C</th>
    <th>ACC</th>
    <th>F1</th>
    <th>INC (.)</th>
  </tr>
  <tr>
    <td>CoT</td>
    <td>3</td>
    <td>3</td>
    <td>77.6</td>
    <td>69.8</td>
    <td>63.4</td>
  </tr>
  <tr>
    <td>CoT</td>
    <td>12</td>
    <td>12</td>
    <td>78.9</td>
    <td>72.2</td>
    <td>60.0</td>
  </tr>
  <tr>
    <td>CCP</td>
    <td>3</td>
    <td>11</td>
    <td>78.7</td>
    <td>81.7</td>
    <td>57.7</td>
  </tr>
  <tr>
    <td>CCP</td>
    <td>12</td>
    <td>26</td>
    <td><b>85.0</b></td>
    <td><b>82.2</b></td>
    <td><b>49.8</b></td>
  </tr>
</table>

Table 3: Performance comparison of Llama-3-8B on MCTACO with the different number of ICL examples.

4 Conclusion

We targeted the temporal inconsistency in relative event understanding with LLMs by proposing a prompting approach using counterfactual questions. This encourages the model to focus more on the temporal aspects and collectively evaluate its answer with imposed constraints. Experiments with the INC metric show that our approach mitigates inconsistency and improves overall performance.

5 Limitation

Our method showed limited performance improvement when time indicators, such as specific years
(e.g., 1980), are involved in temporal understanding. This is implied from our evaluations on event-time ordering and time-time ordering tasks, as shown in Appendix D.1. The findings suggest that arithmetic reasoning is essential for grounding timelines with absolute time indicators, as emphasized in prior studies (Su et al., 2024; Zhu et al., 2023).

Another limitation is that we focused on pointwise and pairwise event reasoning to highlight the model’s struggles with basic temporal reasoning due to consistency issues. We anticipate future work expanding our approach to more complex list-wise ordering like event schema prediction (Zhang et al., 2024).

Finally, the effectiveness of LLMs can be impacted by the specific wording of prompts (Jiang et al., 2020). For example, Appendix D.2 shows that, although our revised prompts generally yield better results than CoT, CCP experienced a slight decrease in performance.

Acknowledgement

This work was supported by Naver, the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. RS-2024-00414981), Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No. 2022-0-00077/RS-2022-II220077, AI Technology Development for Commonsense Extraction, Reasoning, and Inference from Heterogeneous Data), and Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government(MSIT) [NO.RS-2021-II211343, Artificial Intelligence Graduate School Program (Seoul National University)].

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Appendices

A Data Summary

Table 4 summarizes the dataset statistics used in this study. The numbers of official test samples are reported. Due to the budget, we evaluated Llama-3-8B on the full test set, GPT-4o-mini and Llama-3-70B on a random sample of up to 2,000 test set instances, and GPT-4o on 1,000 test set instances.

Additionally, the number of temporal relations considered in each dataset is included in Table 4. TempEvalQA-Bi and TRACIE focus mainly on the before-after relation. MCTACO includes diverse temporal relations, and the number of annotated candidates is reported. The questions in MCTACO are categorized into 5 question types, and examples for each type are provided in Figure 4.

<table>
  <tr>
    <th></th>
    <th>#Test</th>
    <th>#Temporal relations</th>
  </tr>
  <tr>
    <td>TempEvalQA-Bi</td>
    <td>448</td>
    <td>2</td>
  </tr>
  <tr>
    <td>TRACIE</td>
    <td>4248</td>
    <td>2</td>
  </tr>
  <tr>
    <td>MCTACO</td>
    <td>9442</td>
    <td>1-19</td>
  </tr>
</table>

Table 4: Dataset Statistics. For TempEvalQA-Bi, the numbers represent the total number of questions. For TRACIE, the numbers refer to the number of story-hypothesis pairs. For MCTACO, the numbers reflect question-and-answer candidate pairs.

B Details of Evaluation Settings

This section outlines the detailed evaluation settings, including hyperparameters, resources, efficiency, and parsing methods. We use greedy decoding for SP, CoT, and CCP. For Consistency, Reflect, and Debate, we adopt the approach from Wang et al. (2023), employing top-k sampling with \( k = 40 \) and a temperature of 0.5 for the LLaMA model. For GPT-based models, we set the temperature to 0.7. Consistency samples 40 outputs from the decoder. Reflect refines the output iteratively for two iterations, including the initial output. In Debate, three agents engage in a debate over two rounds(Du et al., 2024). The implementations of the latter two baselines (Reflect, Debate) are based on the GitHub repository ¹ from Du et al. (2024). Single-run performances are reported.

We note that our method prompts 3 times: for counterfactual question generation, counterfactual answer generation, and original question’s answer generation, whose efficiency is compatible with or even more efficient than the three baselines. We also note that the Consistency baseline of Llama-3-70B cannot be reported due to its computation inefficiency.

For resources, we used the Transformers library (Wolf et al., 2020) and vLLM (Kwon et al., 2023) with 4 RTX A6000 GPUs for Llama-3 models. We used Openai API ² for GPT models. For output parsing, the models generate the final answer after the phrase “Final answer:”. Counterfactual exemplars are generated by modifying each dataset’s questions, hypotheses, and candidate answers.

<table>
  <tr>
    <th colspan="2">Event Duration</th>
  </tr>
  <tr>
    <td>P. However, more recently, it has been suggested that it may date from earlier than Abdalonymus’ death.</td>
    <td>Q. How long has it existed?</td>
  </tr>
  <tr>
    <td>(A) 2,000 hours (B) 2,000 years (C) 1 year<br>(D) thousands of years (E) centuries (F) months</td>
    <td></td>
  </tr>
  <tr>
    <th colspan="2">Event Frequency</th>
  </tr>
  <tr>
    <td>P. Most of us have seen steam rising off a wet road after a summer rainstorm.</td>
    <td>Q. How often does it rain in the summer?</td>
  </tr>
  <tr>
    <td>(A) 333.33 times (B) every other minute (C) a couple times<br>(D) every month (E) once a hour (F) once a year</td>
    <td></td>
  </tr>
  <tr>
    <th colspan="2">Stationarity</th>
  </tr>
  <tr>
    <td>P. She renews in Ranchipur an acquaintance with a former lover , Tom Ransome , now a dissolute alcoholic.</td>
    <td>Q. Is she still in Ranchipur?</td>
  </tr>
  <tr>
    <td>(A) yes (B) no</td>
    <td></td>
  </tr>
  <tr>
    <th colspan="2">Event Ordering</th>
  </tr>
  <tr>
    <td>P. Some of the people who took advantage of her through a questionable loan program were sent to jail.</td>
    <td>Q. What happened after they were put in jail?</td>
  </tr>
  <tr>
    <td>(A) they went to the store (B) they repented<br>(C) even some people took these steps</td>
    <td></td>
  </tr>
  <tr>
    <th colspan="2">Typical Time</th>
  </tr>
  <tr>
    <td>P. Durer’s father died in 1502, and his mother died in 1513.</td>
    <td>Q. When did Durer die?</td>
  </tr>
  <tr>
    <td>(A) 40 years later (B) 360 years later (C) 4545<br>(D) 40 seconds later (E) April 6, 1528</td>
    <td></td>
  </tr>
</table>

Figure 4: Examples of MCTACO Question Types. MCTACO covers various temporal aspects including event duration, frequency, stationarity, ordering, and typical time.

¹https://github.com/composable-models/llm_multiagent_debate
²platform.openai.com
<table>
  <tr>
    <th>Models</th>
    <th>Methods</th>
    <th colspan="2">MCTACO</th>
  </tr>
  <tr>
    <th></th>
    <th></th>
    <th>EM</th>
    <th>F1</th>
  </tr>
  <tr>
    <td>GPT-4o-mini</td>
    <td>MCQA-CoT<br>CCP</td>
    <td>51.7<br><b>58.9</b></td>
    <td>67.7<br><b>78.6</b></td>
  </tr>
  <tr>
    <td>GPT-4o</td>
    <td>MCQA-CoT<br>CCP</td>
    <td>65.6<br><b>66.2</b></td>
    <td>73.3<br><b>80.2</b></td>
  </tr>
</table>

Table 5: Performance comparison on MCTACO with multiple-choice question answering setting.

C Further Analysis

C.1 Task generalizability
To demonstrate that our solution extends beyond binary question answering to multiple-choice question answering (MCQA), we evaluated the performance of GPT models using the original MCTACO evaluation setting (Zhou et al., 2019). While our primary evaluation decomposed the multiple-choice format into binary questions to measure inconsistency, it can be reconstructed for multiple-choice evaluation. We additionally introduced a baseline for MCQA (MCQA-CoT) that provides the context, question, and all candidate answers, generating one or more correct answers step-by-step. The results in Table 5 indicate that our method (CCP) outperforms the MCQA-CoT baseline on multiple-choice tasks, demonstrating its effectiveness in the MCQA setting.

C.2 Generated vs Retrieved Questions

![Comparison between counterfactual example collection methods on MCTACO with different models.](page_120_670_627_246.png)

Figure 5: Comparison between counterfactual example collection methods on MCTACO with different models.

We tested whether our claim in Figure 2 can be generalized to other models. Figure 5 consistently confirms that creating counterfactual questions by generation handles diverse temporal relations better than retrieving questions across different models.

C.3 Number of Counterfactual Questions
We analyze the impact of varying the number of counterfactual questions on performance by testing with 1, 3, 5, and 7 questions. As shown in Figure 6,

![Inconsistency changes with the different number of counterfactual questions. The Llama-3-8B model is used.](page_820_670_627_246.png)

Figure 6: Inconsistency changes with the different number of counterfactual questions. The Llama-3-8B model is used.

performance is highest with a single counterfactual question, with degradation observed as the number increases. The result aligns with findings from prior studies, where incorporating excessive counterfactual or contrastive information in prompts often results in diminished performance (Yao, 2024; Fang et al., 2024; Storai and Hwang, 2024). For instance, multiple information degrade the performance in arithmetic and symbolic reasoning (Yao, 2024), multi-hop and commonsense question answering (Fang et al., 2024), and speculative decoding (Storai and Hwang, 2024). These results indicate that such a phenomenon is not specific to our method but highlights a broader limitation in LLMs’ ability to process multiple counterfactual information effectively.

<table>
  <tr>
    <th rowspan="2"></th>
    <th colspan="2">TimeQA</th>
    <th colspan="2">TimexNLI</th>
  </tr>
  <tr>
    <th>ACC</th>
    <th>F1</th>
    <th>ACC</th>
    <th>F1</th>
  </tr>
  <tr>
    <td>Llama 3-8B</td>
    <td>3 shot</td>
    <td><b>34.3</b></td>
    <td>40.8</td>
    <td>68.0</td>
    <td>65.3</td>
  </tr>
  <tr>
    <td></td>
    <td>CoT 3 shot</td>
    <td>32.3</td>
    <td>38.4</td>
    <td>74.0</td>
    <td><b>73.3</b></td>
  </tr>
  <tr>
    <td></td>
    <td>CCP 3 shot</td>
    <td>34</td>
    <td><b>41.5</b></td>
    <td>67.3</td>
    <td>62.2</td>
  </tr>
  <tr>
    <td>GPT-4o-mini</td>
    <td>3 shot</td>
    <td>40</td>
    <td>52.36</td>
    <td>86.4</td>
    <td>85.3</td>
  </tr>
  <tr>
    <td></td>
    <td>CoT 3 shot</td>
    <td><b>43.3</b></td>
    <td><b>56.75</b></td>
    <td><b>90.4</b></td>
    <td><b>90.3</b></td>
  </tr>
  <tr>
    <td></td>
    <td>CCP 3 shot</td>
    <td>41</td>
    <td>53.59</td>
    <td>90.3</td>
    <td>90.0</td>
  </tr>
</table>

Table 6: Performance comparison on TimeQA and TimexNLI.

D Details of Limitations

D.1 Tasks with temporal indicators
Table 6 shows the experimental results for the tasks requiring the understanding of temporal indicators. We evaluated our method on TimeQA (Chen et al., 2021), the event-time ordering task, and TimexNLI-T1 (Thukral et al., 2021), the time-time ordering task, where CCP showed limited perfor-
D.2 Prompt Sensitivity

Our key decision in the prompt design was to separate the counterfactual question generation prompt (CCP), described in Appendix F.1, from the prompt that answers counterfactual and original questions, detailed in Appendix F.2. If we generate counterfactual questions and answers in an end-to-end manner using only the prompt in Appendix F.2 (CCP(e2e)), while it still outperforms CoT, the performance slightly decreases, as shown in Table 7.

E Usage of AI Assistants

ChatGPT was employed to generate answers in the prompt examples.

F Prompt Templates

We list the prompts that we used.

F.1 Prompt Templates for Generating Counterfactual Questions

To generate the counterfactual questions, we use the prompts provided below. We control question aspects by tailoring ICL examples and prompting the model to follow few-shot examples with the prompt: ("following previous examples").

TempEvalQA-Bi

[System]
You are an expert in temporal knowledge. Generate one related question to help determine the correctness of the original question, following the previous examples.
[User]
Question: Is Farkas sent into space on board the Soyuz before McBride on board the Orbiter Challenger?
[Assistant]
Is Farkas sent into space on board the Soyuz after McBride on board the Orbiter Challenger?
[User]
Question: Is McBride on board the Orbiter Challenger after Farkas was made a brigadier general?
[Assistant]
Is McBride on board the Orbiter Challenger before Farkas was made a brigadier general?
[User]
Question: Is Farkas was appointed military attache at the Hungarian embassy before he was made a brigadier?
[Assistant]
Is Farkas was appointed military attache at the Hungarian embassy after he was made a brigadier?

TRACIE

[System]
You are an expert in temporal knowledge. Generate one related hypothesis to help determine the plausibility of the original hypothesis, following previous examples.
[User]
<table>
  <tr>
    <th rowspan="2">Models</th>
    <th rowspan="2">Prompts</th>
    <th colspan="3">TempEvalQA-Bi</th>
    <th colspan="3">TRACIE</th>
    <th colspan="3">MCTACO</th>
  </tr>
  <tr>
    <th>ACC</th>
    <th>F1</th>
    <th>INC</th>
    <th>ACC</th>
    <th>F1</th>
    <th>INC</th>
    <th>ACC</th>
    <th>F1</th>
    <th>INC</th>
  </tr>
  <tr>
    <td rowspan="3">Llama-3-8B</td>
    <td>CoT</td>
    <td>69.6</td>
    <td>70.6</td>
    <td>50.0</td>
    <td>63.0</td>
    <td>64.9</td>
    <td>56.0</td>
    <td>77.6</td>
    <td>69.8</td>
    <td>63.4</td>
  </tr>
  <tr>
    <td>CCP (e2e)</td>
    <td>75.4</td>
    <td>73.6</td>
    <td>33.9</td>
    <td>66.8</td>
    <td>65.4</td>
    <td>46.7</td>
    <td>83.1</td>
    <td>81.0</td>
    <td>53.7</td>
  </tr>
  <tr>
    <td>CCP</td>
    <td>75.9</td>
    <td>75.2</td>
    <td>32.7</td>
    <td>68.8</td>
    <td>70.4</td>
    <td>39.8</td>
    <td>78.7</td>
    <td>81.7</td>
    <td>57.7</td>
  </tr>
  <tr>
    <td rowspan="3">GPT-4o-mini</td>
    <td>CoT</td>
    <td>81.3</td>
    <td>79.9</td>
    <td>29.0</td>
    <td>73.2</td>
    <td>68.5</td>
    <td>42.7</td>
    <td>80.9</td>
    <td>73.7</td>
    <td>58.9</td>
  </tr>
  <tr>
    <td>CCP (e2e)</td>
    <td>80.8</td>
    <td>80.2</td>
    <td>27.7</td>
    <td>79.0</td>
    <td>78.3</td>
    <td>28.0</td>
    <td>87.1</td>
    <td>84.4</td>
    <td>52.1</td>
  </tr>
  <tr>
    <td>CCP</td>
    <td>88.8</td>
    <td>88.7</td>
    <td>19.6</td>
    <td>82.5</td>
    <td>81.2</td>
    <td>20.2</td>
    <td>87.8</td>
    <td>85.8</td>
    <td>42.1</td>
  </tr>
</table>

Table 7: Performance comparison with different prompts. The best and second-best performances are in boldface and underlined, respectively.

Hypothesis: Chad looked for his baseball cap starts after he got off the ride.
[Assistant]
Chad looked for his baseball cap starts before he got off the ride.
[User]
Hypothesis: Tom’s friend says he is not gay starts before One day he noticed someone else asking
[Assistant]
Tom’s friend says he is not gay starts after One day he noticed someone else asking
[User]
Hypothesis: Liza read a book on economics in the library starts before she got to the library
[Assistant]
Liza read a book on economics in the library starts after she got to the library

[Assistant]
The Ottoman Empire had just begun / The spread of Byzantine influence in the region / The emergence of Islam as a minor religion
[User]
Passage: It’s hail crackled across the comm, and Tara spun to retake her seat at the helm. Question: How long was the storm? Candidate answer: 6 years.
[Assistant]
an hour / a week / a month
[User]
Passage: Passage: About 30% of Ratners’s profit already is derived from the U.S. Question: Is Ratners’s profit derived from the U.S. today? Candidate answer: yes.
[Assistant]
no

MCTACO
[System]
You are an expert in temporal commonsense knowledge. Generate related candidate answers that are either plausible or implausible that help determine the correctness of the original candidate answer following the previous examples.
[User]
Passage: The majority religion during the centuries of Ottoman rule, though a significant Christian minority remained. Question: What happened before Islam was the majority religion? Candidate answer: christianity was the majority religion.

F.2 Prompt Templates for CCP and Baselines

We only show the SP, CoT, and CCP since Consistency is the method that leverages CoT multiple times, and the Reflect and Debate follow the implementation of Du et al. (2024) after CoT.

Given the system and user message, the model generates an assistant’s message. In our approach, the model is prompted twice: first to create an assistant’s answer to the counterfactual question, and then to generate an assistant’s answer to the original question. Though we use 3-shot examples, we provide 1 example for simplicity.

Prompt templates used to generate answers for the TempevalQA-Bi dataset are provided below.
TempevalQA-Bi: SP
[System]
You are an expert in temporal knowledge. Answer the question according to the article. Answer the question yes or no (Format: final answer: yes/no)
[User]
Article: Farkas, an air force captain, was sent into space on board the Soyuz 36 on May 26, 1980. He spent six days aboard the Salyut 6 spacecraft with three Soviet astronauts, Valery Kubasov, Leonid Popov and Valery Riumin. McBride, 54, of Lewisburg, West Virginia, was part of a seven-member crew aboard the Orbiter Challenger [...]
Question: Is Farkas sent into space on board the Soyuz before McBride on board the Orbiter Challenger?
[Assistant]
Final answer: yes

questions as the additional information, answer the original question yes or no (Format: final answer: [yes/no]).
[User]
Article: [...]
Original question: Is Farkas sent into space on board the Soyuz before McBride on board the Orbiter Challenger?
Related question: Is Farkas sent into space on board the Soyuz after McBride on board the Orbiter Challenger?
Answer the related question
[Assistant] # Prediction for the counterfactual question
Farkas was sent into space on board the Soyuz 36 on May 26, 1980. McBride was part of the crew on board the Orbiter Challenger in October 1984. Since 1980 is before 1984, no, Farkas was not sent into space after McBride.
answer: no
[User]
Now, answer the original question. Question: Is Farkas sent into space on board the Soyuz before McBride on board the Orbiter Challenger?
[Assistant] # Prediction for the original question
Farkas was sent into space on May 26, 1980 and McBride was on board the Orbiter Challenger in October 1984. May 26, 1980 is before October 1984. So the answer is: yes.
Final answer: yes

TempevalQA-Bi: CoT
[System]
You are an expert in temporal knowledge. Answer the question according to the article. Let’s think step by step to answer the question. The answer should be "yes" or "no" followed by "Final answer: ".
[User]
Article: [...]
Question: Is Farkas sent into space on board the Soyuz before McBride on board the Orbiter Challenger?
[Assistant]
Let’s think step by step. Farkas was sent into space on May 26, 1980 and McBride was on board the Orbiter Challenger in October 1984. May 26, 1980 is before October 1984. So the answer is: yes.
Final answer: yes

TempevalQA-Bi: CCP
[System]
You are an expert in temporal knowledge. Answer the question according to the article. To improve understanding, follow these steps: Answer the related question to better understand the timeline (Format: answer: [yes/no]) Using the answers to the related

Prompt templates used to generate answers for the TRACIE dataset are provided below.

TRACIE: SP
[System]
You are an expert in temporal knowledge. You can understand the implicit temporal relationships between events to make judgments. Your task is to determine the relationship between the story and hypothesis. A ‘positive’ label means the hypothesis can be inferred from the story or logically sound. A ‘negative’ label means the hypothesis cannot be inferred from the story. You must answer only with the labels ‘positive’ or ‘negative’. (Format: final answer: posi-
tive/negative)
[User]
Story: Chad looked for his baseball cap starts after he got off the ride story: Chad had gone to an amusement park. He was riding on the roller coaster.
Hypothesis: Chad looked for his baseball cap starts after he got off the ride.
[Assistant]
Final answer: positive

TRACIE: CoT
[System]
You are an expert in temporal knowledge. You can understand the implicit temporal relationships between events to make judgments. Your task is to determine the relationship between the story and hypothesis. A ‘positive’ label means the hypothesis can be inferred from the story or logically sound. A ‘negative’ label means the hypothesis cannot be inferred from the story. You must give final answer only with the labels ‘positive’ or ‘negative’ after the “Final answer:” prompt. Let’s think step by step to evaluate the relationship.
[User]
Story: [...]
Hypothesis: Chad looked for his baseball cap starts after he got off the ride.
[Assistant]
Let’s think step by step:
The story states that Chad’s baseball cap fell off during the roller coaster ride.
It also mentions that Chad found the cap after he got off the ride. To find something, one typically needs to look for it first. Since Chad found the cap after getting off the ride, he must have started looking for it after getting off the ride. The hypothesis directly aligns with this sequence of events.
Final answer: positive

relationship between the story and hypothesis. A ‘positive’ label means the hypothesis can be inferred from the story or logically sound. A ‘negative’ label means the hypothesis cannot be inferred from the story. You must give final answer only with the labels ‘positive’ or ‘negative’. To improve understanding, follow these steps: Evaluate the related hypothesis to help clarify the story’s timeline (Format: answer: [positive/negative]). Using answers to the related hypothesis as the additional information, evaluate the original hypothesis (Format: final answer: [positive/negative]).
[User]
Story: [...]
Hypothesis: Chad looked for his baseball cap starts after he got off the ride.
Related hypothesis: Chad looked for his baseball cap starts before he got off the ride.
Answer the related hypothesis
[Assistant] # Prediction for the counterfactual question
The hypothesis conflicts with the story, as Chad finds the cap after the ride.
Answer: negative
[User]
Now, evaluate the original hypothesis: Chad looked for his baseball cap starts after he got off the ride.
[Assistant] # Prediction for the original question
Chad rides the roller coaster while wearing a baseball cap, which falls off during the ride. After getting off the ride, Chad finds the cap. The hypothesis suggests that Chad started looking for the cap after getting off the ride, which aligns with the story’s sequence of events.
Final answer: positive

Prompt templates used to generate answers for the MCTACO dataset are provided below.

TRACIE: CCP
[System]
You are an expert in temporal knowledge. You can understand the implicit temporal relationships between events to make judgments. Your task is to determine the re-

MCTACO: SP
[System]
You are expert in temporal commonsense knowledge. Your goal is to determine if the candidate answer to a given question is plausible based on the information in
the passage. Answer the related candidate answers then answer the candidate answer. Provide a ‘yes’ or ‘no’ response to indicate whether the original candidate answer is correct. (Format: final answer: yes/no) If the passage does not provide explicit details, provide an educated guess based on what is common or plausible in similar situations

[User]
Passage: the majority religion during the centuries of Ottoman rule, though a significant Christian minority remained.
Question: What happened before Islam was the majority religion?
Candidate answer: the end of white-minority rule.
[Assistant]
Final answer: no

MCTACO: CoT
[System]
You are an expert in temporal commonsense knowledge. Your goal is to determine if the candidate answer to a given question is plausible based on the information in the passage. Let’s think step by step and provide a final ‘yes’ or ‘no’ response to indicate whether the original candidate answer is correct. If the passage does not provide explicit details, provide an educated guess based on what is common or plausible in similar situations. The final answer should be in the format: “Final answer: yes” or “Final answer: no”.

[User]
Passage: the majority religion during the centuries of Ottoman rule, though a significant Christian minority remained.
Question: What happened before Islam was the majority religion?
Candidate answer: christianity was the majority religion
[Assistant]
Let’s think step by step.
Step 1: Analyze the passage. The passage states that during the centuries of Ottoman rule, Islam was the majority religion, while a significant Christian minority remained. This implies that before the Ottoman Empire (which was Islamic), there could have been a different majority religion.
Step 2: Historical context. Before the rise of the Ottoman Empire, large parts of the Middle East, North Africa, and parts of Europe were under the rule of the Byzantine Empire, which was a Christian empire. Additionally, many regions that later came under Ottoman rule were predominantly Christian.
Step 3: Plausibility of the candidate answer. Given that Christianity was the dominant religion in many regions before the Ottoman Empire and its Islamic rule, it is plausible that Christianity was the majority religion before Islam in those areas.
Final answer: yes

MCTACO: CCP
[System]
You are an expert in temporal commonsense knowledge. Your goal is to determine if the candidate answer to a given question is plausible based on the information in the passage. To improve understanding, follow these steps: generate related candidate answers that are either plausible or implausible (Format: answer: yes/no) to help in determining the correctness of the original candidate answer. Provide a ‘yes’ or ‘no’ response to indicate whether the original candidate answer is correct (Format: final answer: yes/no). If the passage does not provide explicit details, provide an educated guess based on what is common or plausible in similar situations

[User]
Passage: the majority religion during the centuries of Ottoman rule, though a significant Christian minority remained.
Question: What happened before Islam was the majority religion?
original candidate answer: christianity was the majority religion
Related candidate: the end of white-minority rule
Can the candidate answer the given question? yes or no
[Assistant] # Prediction for the counterfactual question
This is incorrect because the passage dis-
cusses events during Ottoman rule, not before it.
answer: no
[User]
Now, can the candidate answer the given question? candidate answer: christianity was the majority religion
[Assistant] # Prediction for the original question
This is plausible because Islam would have started to emerge before becoming the majority.
Final answer: yes

G  Scientific Artifacts

We used existing scientific artifacts for research purposes, and the use of existing artifacts was consistent with their intended applications.
    TempEvalQA-Bi: MIT license
    TRACIE: Apache-2.0 license
    Llama-3: custom commercial license
    OpenAI API: Apache-2.0 license

Reviewer paper summaries: This paper presents an innovative method to elicit the temporal inconsistency of Large Language Models by using a unique counterfactual prompting strategy. The authors achieved this by generating temporally counterfactual questions to train the language model, with the question set being dynamically generated by models. The paper also utilizes three benchmark datasets for their method evaluation.
Summary of strengths: Introduces a novel method to elicit the temporal inconsistency of LLMs.
•	Introduction of a new evaluation metric, ‘the inconsistency metric (INC)’.
•	Several prompt comparison techniques used within the same model provide a good comparison of the proposed CCP technique.
•	Task generalization by leveraging a baseline for MCQA, the MCQA-CoT that provides the context, question, and all candidate answers.
Summary of weaknesses: The number of baselines compared are less. Few more comparisons on different LLMs would have provided a clearer evaluation of the proposed method.
•	The models GPT-4o-mini and Llama3-70B were evaluated on a subset of 2000 samples only while GPT-4o was evaluated on 1000 samples only.
•	The proposed method CCP  shows limited performance variations in time-ordering tasks.
Comments, suggestions and typos: NA
Overall assessment scores: 3
Metareview score: 3.5
Metareview: The authors propose a prompt construction method for Temporal Understanding. The paper clearly presents its innovative contributions, and the authors have adequately addressed the reviewers' feedback. However, my concerns align with those raised by Reviewer FuMb:
a. Lack of comparison with fine-tuning methods—while the authors emphasize that this work focuses on non-finetuned approaches, such a comparison remains important for context.
b. Uncertainty about real-world task reliability—the method’s performance in practical scenarios needs further validation.
Summary of reasons to publish: Strengths: Introduces a novel approach and demonstrates its effectiveness.