## 6 Experimental Results and Discussion
### Comparison with Baselines  
In this section, the reasoning results of the baselines and the proposed method on five datasets are compared and analyzed. The main results are shown in Tables 2 and 3 (in Tables 2 and 3, the results of rows 1 to 3 are quoted from [42]. The results of rows 4 to 6 are obtained from the original papers [27, 28, 30]. The results of rows 7 and 8 are obtained by our implementation) and the best results are marked in bold. In Table 2 and 3, the results in rows 1-2 are obtained by distributed representation learning models, and the rows 3-4 are the performance of the logical rules learning methods. Rows 5-7 display the performance of the pre-trained language models and the large language models. The results in row 8 are obtained by our proposed method. * Comparing the results in rows 1-4 (traditional methods) and rows 5-8 (pre-trained language model- and large language model-based methods) in two tables, among 15 metrics, the 10 best results are obtained by the language model-based methods. These results demonstrate that employing a large language model can enhance the performance of knowledge graph reasoning. One reason could be that compared to reasoning based on limited knowledge graph triples, pre-trained language models contain more extensive knowledge, which is more conducive to completing the reasoning process. * Considering the results in rows 5-6 and rows 7-8 of the two tables, most of the performances in rows 7-8 are better than rows 5-6. The reason may be that the methods GPT\({}_{one-shot}\) and RuleLLM employ in-context learning in reasoning, which can help LLMs to comprehend the given reasoning task and further improve the reasoning performance. These results validate the importance and effectiveness of in-context learning for LLMs on reasoning. * Our proposed method performs the best on three datasets (WN18 RR, FB15k-237, and Wikidata5m). Compared with traditional reasoning methods, the greatest improvement is 0.147 on Hits@10 for FB15k-237 (compared with the model AnyBURL). These results demonstrate the effectiveness of our proposed method. One reason may be that the proposed rule-and-reinforce in-context triple selection method is able to extract better in-context examples with respect to the specific reasoning task, providing more helpful factual evidence for reasoning. Although the experimental results show that the proposed method can achieve certain improvements, there are still several limitations: (1) First, the reasoning results entirely depend on the output of LLMs, which suffer from hallucination issues. Therefore, even if the in-context triples are correct, the reasoning results may still be wrong. This is one of the limitations of the proposed method. In the future, we should focus on retrieving more accurate in-context triples on the one hand, and processing the outputs of the LLMs on the other hand, to further improve the quality of the reasoning results. (2) In addition, in this method, one of the important bases for exploring the in-context triples are the logical rules, which are mainly obtained through probabilistic methods by analyzing the frequent patterns. In practical applications, the logical rules used are not always appropriate for the given reasoning task. This is another limitation of the proposed method. Therefore, considering more reasoning factors to improve the accuracy of extracting in-context triples is also one of the directions that is worth further investigation.