  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.
