Probabilistic logical rule learning has shown great strength in logical rule mining and knowledge graph completion. It learns logical rules to predict missing edges by reasoning on existing edges in the knowledge graph. However, previous efforts have largely been limited to only modeling chain-like Horn clauses such as $R_1(x,z)\land R_2(z,y)\Rightarrow H(x,y)$. This formulation overlooks additional contextual information from neighboring sub-graphs of entity variables $x$, $y$ and $z$. Intuitively, there is a large gap here, as local sub-graphs have been found to provide important information for knowledge graph completion. Inspired by these observations, we propose Logical Entity RePresentation (LERP) to encode contextual information of entities in the knowledge graph. A LERP is designed as a vector of probabilistic logical functions on the entity's neighboring sub-graph. It is an interpretable representation while allowing for differentiable optimization. We can then incorporate LERP into probabilistic logical rule learning to learn more expressive rules. Empirical results demonstrate that with LERP, our model outperforms other rule learning methods in knowledge graph completion and is comparable or even superior to state-of-the-art black-box methods. Moreover, we find that our model can discover a more expressive family of logical rules. LERP can also be further combined with embedding learning methods like TransE to make it more interpretable.

翻译：概率逻辑规则学习在逻辑规则挖掘和知识图谱补全方面展示了强大的能力。它通过推理知识图谱中已有的边来学习逻辑规则，以预测缺失的边。然而，先前的工作很大程度上局限于仅对链状霍恩子句（如$R_1(x,z)\land R_2(z,y)\Rightarrow H(x,y)$）进行建模。这种形式忽略了来自实体变量$x$、$y$和$z$的邻接子图的额外上下文信息。直观上，这里存在一个很大的差距，因为局部子图已被发现能为知识图谱补全提供重要信息。受这些观察的启发，我们提出了逻辑实体表示（Logical Entity RePresentation，LERP）来编码知识图谱中实体的上下文信息。LERP被设计为一个实体邻接子图上概率逻辑函数的向量。它是一种可解释的表示，同时允许可微优化。然后，我们可以将LERP融入概率逻辑规则学习中，以学习更具表达力的规则。实验结果表明，采用LERP后，我们的模型在知识图谱补全中优于其他规则学习方法，并且与最先进的黑盒方法相比性能相当甚至更优。此外，我们发现我们的模型能够发现更具表达力的逻辑规则家族。LERP还可以进一步与诸如TransE之类的嵌入学习方法相结合，使其更具可解释性。