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Graph Neural Networks (GNNs) have been recently introduced to learn fromknowledge graph (KG) and achieved state-of-the-art performance in KG reasoning.However, a theoretical certification for their good empirical performance isstill absent. Besides, while logic in KG is important for inductive andinterpretable inference, existing GNN-based methods are just designed to fitdata distributions with limited knowledge of their logical expressiveness. Wepropose to fill the above gap in this paper. Specifically, we theoreticallyanalyze GNN from logical expressiveness and find out what kind of logical rulescan be captured from KG. Our results first show that GNN can capture logicalrules from graded modal logic, providing a new theoretical tool for analyzingthe expressiveness of GNN for KG reasoning; and a query labeling trick makes iteasier for GNN to capture logical rules, explaining why SOTA methods are mainlybased on labeling trick. Finally, insights from our theory motivate thedevelopment of an entity labeling method for capturing difficult logical rules.Experimental results are consistent with our theoretical results and verify theeffectiveness of our proposed method.

Logical Expressiveness of Graph Neural Network for Knowledge Graph Reasoning