Rule learning is critical to improving knowledge graph (KG) reasoning due to their ability to provide logical and interpretable explanations. Recently, Graph Neural Networks (GNNs) with tail entity scoring achieve the state-of-the-art performance on KG reasoning. However, the theoretical understandings for these GNNs are either lacking or focusing on single-relational graphs, leaving what the kind of rules these GNNs can learn an open problem. We propose to fill the above gap in this paper. Specifically, GNNs with tail entity scoring are unified into a common framework. Then, we analyze their expressivity by formally describing the rule structures they can learn and theoretically demonstrating their superiority. These results further inspire us to propose a novel labeling strategy to learn more rules in KG reasoning. Experimental results are consistent with our theoretical findings and verify the effectiveness of our proposed method. The code is publicly available at https://github.com/LARS-research/Rule-learning-expressivity.

翻译：规则学习对提升知识图谱推理能力至关重要，因其能提供逻辑化且可解释的推理路径。近年来，采用尾实体评分机制的图神经网络在知识图谱推理任务中取得了最先进的性能。然而，现有针对这类图神经网络的理论研究要么缺失，要么聚焦于单关系图，导致这类网络所能学习的规则类型仍是一个开放性问题。本文旨在填补上述研究空白。具体而言，我们将采用尾实体评分机制的图神经网络统一纳入一个通用框架，进而通过形式化描述其可学习的规则结构并理论证明显著性来解析其表达能力。这些结论进一步启发我们提出一种新型标注策略，以在知识图谱推理中学习更多规则。实验结果与理论发现高度吻合，验证了所提方法的有效性。代码已开源至 https://github.com/LARS-research/Rule-learning-expressivity。