LOGICAL ENTITY REPRESENTATION IN KNOWLEDGE-GRAPHS FOR DIFFERENTIABLE RULE LEARNING

Abstract

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) ∧ R 2 (z, y) ⇒ 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. 1

1. INTRODUCTION

In recent years, the use of logical formulation has become prominent in knowledge graph (KG) reasoning and completion (Teru et al., 2020; Campero et al., 2018; Payani & Fekri, 2019) , mainly because a logical formulation can be used to enforce strong prior knowledge on the reasoning process. In particular, probabilistic logical rule learning methods (Sadeghian et al., 2019; Yang et al., 2017) have shown further desirable properties including efficient differentiable optimization and explainable logical reasoning process. These properties are particularly beneficial for KGs since KGs are often large in size, and modifying KGs has social impacts so rationales are preferred by human readers. Due to the large search space of logical rules, recent efforts Sadeghian et al. ( 2019  r 1 (x, z 1 ) ∧ r 2 (z 1 , z 2 ) ∧ • • • ∧ r K (z K-1 , y) ⇒ H(x, y), where r k represents relations and x, y z k represent entities in the graph. Even though this formulation is computationally efficient (see Section 3), it overlooks potential contextual information coming from local sub-graphs neighboring the entities (variables x, y, and all z i ). However, this kind of contextual information can be important for reasoning on knowledge graphs. Figure 1 (b) shows an example. If we only know that z is mother of x and y, we are not able to infer if y is a brother or sister of x. However, in Figure 1 (c), with the contextual logical information that ∃z is son of(y, z ) we can infer that y is a male and that y should be the brother rather than the sister of x.



All code and data are publicly available at https://github.com/Glaciohound/LERP. 1



); Yang et al. (2017); Payani & Fekri (2019) focus on learning chain-like Horn clauses of the following form:

