RULE: NEURAL-SYMBOLIC KNOWLEDGE GRAPH REASONING WITH RULE EMBEDDING

Abstract

Knowledge graph (KG) reasoning is an important problem for knowledge graphs. It predicts missing links by reasoning on existing facts. Knowledge graph embedding (KGE) is one of the most popular methods to address this problem. It embeds entities and relations into low-dimensional vectors and uses the learned entity/relation embeddings to predict missing facts. However, KGE only uses zeroth-order (propositional) logic to encode existing triplets (e.g., "Alice is Bob's wife."); it is unable to leverage first-order (predicate) logic to represent generally applicable logical rules (e.g., "∀x, y : x is y's wife → y is x's husband"). On the other hand, traditional rule-based KG reasoning methods usually rely on hard logical rule inference, making it brittle and hardly competitive with KGE. In this paper, we propose RulE, a novel and principled framework to represent and model logical rules and triplets. RulE jointly represents entities, relations and logical rules in a unified embedding space. By learning an embedding for each logical rule, RulE can perform logical rule inference in a soft way and give a confidence score to each grounded rule, similar to how KGE gives each triplet a confidence score. Compared to KGE alone, RulE allows injecting prior logical rule information into the embedding space, which improves the generalization of knowledge graph embedding. Besides, the learned confidence scores of rules improve the logical rule inference process by softly controlling the contribution of each rule, which alleviates the brittleness of logic. We evaluate our method with link prediction tasks. Experimental results on multiple benchmark KGs demonstrate the effectiveness of RulE. https:

1. INTRODUCTION

Knowledge graphs (KGs) usually store millions of real-world facts and are used in a variety of applications, such as recommender systems (Wang et al., 2018 ), question answering (Bordes et al., 2014) and information retrieval (Xiong et al., 2017) . Examples of knowledge graphs include Freebase (Bollacker et al., 2008 ), WordNet(Miller, 1995) and YAGO (Suchanek et al., 2007) . They represent entities as nodes and relations among the entities as edges. Each edge encodes a fact in the form of a triplet (head entity, relation, tail entity). However, KGs are usually highly incomplete due to the limitedness of human knowledge and web corpora, as well as imperfect extraction algorithms. Knowledge graph reasoning, which predicts missing facts by reasoning on existing facts, has thus become a popular research area in Artificial Intelligence. There are two prominent lines of work in this area: knowledge graph embedding (KGE), which embeds all entities and relations into vectors, and rule-based KG reasoning, which uses logical rules to infer new facts. Knowledge graph embedding (KGE) methods such as TransE (Bordes et al., 2013 ), Com-plEx (Trouillon et al., 2016 ) and RotatE (Sun et al., 2019) have received significant attention due to their effectiveness and scalability. They embed entities and relations into low-dimensional vectors or matrices, preserving the inherent structure and latent semantic information. By computing the score of each triplet in the continuous space, KGE effectively estimates the plausibility of unobserved triplets so that reasoning of missing facts becomes feasible. However, KGE only uses zeroth-order (propositional) logic to encode existing facts (e.g., "Alice is Bob's wife."). It cannot leverage firstorder (predicate) logic, which uses the universal quantifier to represent generally applicable logical † Corresponding authors. 1

availability

//github.com/XiaojuanTang/RulE

