TILP: DIFFERENTIABLE LEARNING OF TEMPORAL LOGICAL RULES ON KNOWLEDGE GRAPHS

Abstract

Compared with static knowledge graphs, temporal knowledge graphs (tKG), which can capture the evolution and change of information over time, are more realistic and general. However, due to the complexity that the notion of time introduces to the learning of the rules, an accurate graph reasoning, e.g., predicting new links between entities, is still a difficult problem. In this paper, we propose TILP, a differentiable framework for temporal logical rules learning. By designing a constrained random walk mechanism and the introduction of temporal operators, we ensure the efficiency of our model. We present temporal features modeling in tKG, e.g., recurrence, temporal order, interval between pair of relations, and duration, and incorporate it into our learning process. We compare TILP with state-of-the-art methods on two benchmark datasets. We show that our proposed framework can improve upon the performance of baseline methods while providing interpretable results. In particular, we consider various scenarios in which training samples are limited, data is biased, and the time range between training and inference are different. In all these cases, TILP works much better than the state-of-the-art methods.

1. INTRODUCTION

Knowledge graphs (KGs) contain facts (e s , r, e o ) representing relation r between subject entity e s and object entity e o , e.g., (David Beckham, plays for, Real Madrid) . In real world, many relations are time-dependent, e.g., a player joining a team for a season, a politician holding a position for a certain period of time, and two persons' marriage lasting for decades. To represent the evolution and change of information, temporal knowledge graphs (tKGs) have been introduced. An interval I, indicating the valid period of the fact, is utilized by tKGs to extend the triples (e s , r, e o ) into quadruples (e s , r, e o , I), e.g., (David Beckham, plays for, Real Madrid, [2003 , 2007] ). Automatically reasoning over KGs such as link predication, i.e., inferring missing facts using existing facts, is a common task for real-world applications. However, the introduction of temporal information makes this task more difficult. The important dynamic interactions between entities can not be captured by learning methods developed for static KGs. Recently, a few embedding-based frameworks have been proposed to address the above limitation, e. 2019)). The common principle adopted by these models is to create time-dependent embeddings for entities and relations. Alternatively, first-order inductive logical reasoning methods have some desirable features relative to embedding methods when applied to KGs, as they provide interpretable and robust inference results. Since the resulting logical rules contain temporal information in tKGs, we call them temporal logical rules. Some recent works, e.g., StreamLearner (Omran et al. (2019) ), and TLogic (Liu et al. ( 2021)), have introduced a framework for temporal KG reasoning. However, there are still several unaddressed issues. First, these statistical methods count from graph the number of paths that support a given rule as its confidence estimation. As such, this independent rule learning ignores the interactions between different rules from the same positive example. For instance, given certain rules, the confidence of some rules might be enhanced, while that of others can be diminished. Sec-



g., HyTE (Dasgupta et al. (2018)), TNTComplEx (Lacroix et al. (2020)), and DE-SimplE (Goel et al. (

