Differentiable Learning of Graph-like Logical Rules from Knowledge Graphs

Logical rules inside a knowledge graph (KG) are essential for reasoning, logical inference, and rule mining. However, existing works can only handle simple, i.e., chain-like and tree-like, rules and cannot capture KG's complex semantics, which can be better captured by graph-like rules. Besides, learning graph-like rules is very difficult because the graph structure exhibits a huge discrete search space. To address these issues, observing the plausibility of logical rules can be explained by how frequently it appears in a KG, we propose a score function that represents graph-like rules with learnable parameters. The score also helps relax the discrete space into a continuous one and can be uniformly transformed into matrix form by the Einstein summation convention. Thus, it allows us to learn graph-like rules in an efficient, differentiable, and end-to-end training manner. We conduct extensive experiments on real-world and synthetic datasets to show that our method outperforms previous works due to logical rules' better expressive ability. Furthermore, we demonstrate that our method can learn high-quality and interpretable graph-like logical rules.