Graph Neural Networks (GNNs) have been recently introduced to learn from knowledge graph (KG) and achieved state-of-the-art performance in KG reasoning. However, a theoretical certification for their good empirical performance is still absent. Besides, while logic in KG is important for inductive and interpretable inference, existing GNN-based methods are just designed to fit data distributions with limited knowledge of their logical expressiveness. We propose to fill the above gap in this paper. Specifically, we theoretically analyze GNN from logical expressiveness and find out what kind of logical rules can be captured from KG. Our results first show that GNN can capture logical rules from graded modal logic, providing a new theoretical tool for analyzing the expressiveness of GNN for KG reasoning; and a query labeling trick makes it easier for GNN to capture logical rules, explaining why SOTA methods are mainly based on labeling trick. Finally, insights from our theory motivate the development of an entity labeling method for capturing difficult logical rules. Experimental results are consistent with our theoretical results and verify the effectiveness of our proposed method.

翻译：图神经网络（GNN）近期被引入用于从知识图谱（KG）中学习，并在知识图谱推理任务中取得了当前最优性能。然而，其优异实证表现的理论证明仍然缺失。此外，尽管逻辑在知识图谱中对于归纳性和可解释性推理至关重要，但现有基于GNN的方法仅旨在拟合数据分布，对其逻辑表达能力的认知十分有限。本文旨在填补上述空白。具体而言，我们从逻辑表达能力角度对GNN进行理论分析，探究GNN能够从知识图谱中捕捉何种逻辑规则。结果表明：GNN能够捕捉来自分级模态逻辑的逻辑规则，这为分析GNN在知识图谱推理中的表达能力提供了新的理论工具；标签查询技巧使GNN更容易捕捉逻辑规则，解释了当前最优方法为何主要基于标签技巧。最后，理论洞见启发我们开发了一种捕捉复杂逻辑规则的实体标注方法。实验结果与理论分析一致，并验证了所提方法的有效性。