Knowledge graph (KG) reasoning is an important problem for knowledge graphs. In this paper, we propose a novel and principled framework called \textbf{RulE} (stands for {Rul}e {E}mbedding) to effectively leverage logical rules to enhance KG reasoning. Unlike knowledge graph embedding (KGE) methods, RulE learns rule embeddings from existing triplets and first-order {rules} by jointly representing \textbf{entities}, \textbf{relations} and \textbf{logical rules} in a unified embedding space. Based on the learned rule embeddings, a confidence score can be calculated for each rule, reflecting its consistency with the observed triplets. This allows us to perform logical rule inference in a soft way, thus alleviating the brittleness of logic. On the other hand, RulE injects prior logical rule information into the embedding space, enriching and regularizing the entity/relation embeddings. This makes KGE alone perform better too. RulE is conceptually simple and empirically effective. We conduct extensive experiments to verify each component of RulE. Results on multiple benchmarks reveal that our model outperforms the majority of existing embedding-based and rule-based approaches.

翻译：知识图谱推理是知识图谱中的一个重要问题。本文提出一个新颖且原理性的框架——**RulE**（即规则嵌入的缩写），旨在有效利用逻辑规则增强知识图谱推理。与知识图谱嵌入方法不同，RulE通过将**实体**、**关系**和**逻辑规则**联合表示在同一嵌入空间中，从现有三元组和一阶规则中学习规则嵌入。基于学习到的规则嵌入，可为每条规则计算置信度分数，反映其与观测三元组的一致性。这使我们能以软性方式执行逻辑规则推理，从而缓解逻辑的脆弱性。另一方面，RulE将先验逻辑规则信息注入嵌入空间，丰富并正则化实体/关系嵌入，这也有助于提升单纯知识图谱嵌入的性能。RulE概念简单且实证有效。我们通过大量实验验证其各组成部分，多个基准测试结果表明，该模型优于现有大多数基于嵌入和基于规则的方法。