Bi-directional Learning of Logical Rules with Type Constraints for Knowledge Graph Completion

Knowledge graph completion (KGC) aims to infer missing facts from existing facts. Learning logical rules plays a pivotal role in KGC, as logical rules excel in explaining why a missing fact is inferred. Most existing rule learning methods focus merely on learning chain-like rules, neglecting type constraints on entities. In practice, type constraints are crucial in expressing precise rules. Therefore, we propose a novel formalism for logical rules named TC-rules, which complements chain-like rules with both explicit and implicit type constraints on entity variables. Accordingly, we propose an end-to-end approach to effectively learn TC-rules, by parameterizing a neural model to simulate the inference of TC-rules. Considering that existing end-to-end methods learn two different sets of logical rules to respectively answer a head query (?,rnew, t) and a tail query (h,rrnew, ?), leading to confusing explanations for supporting a new fact (h,rnew, t), we propose a bi-directional learning mechanism to ensure that the TC-rules learnt for answering (?,rnew, t) are the same as the TC-rules learnt for answering (h,rnew, ?). Experimental results on eight benchmark datasets demonstrate that the proposed method outperforms state-of-the-art rule learners in both the link prediction task and the triple classification task. Furthermore, our case study confirms that expressive TC-rules can be extracted from the parameter assignment of the learnt neural model.