Reasoning over Temporal Knowledge Graphs (TKGs) that predicts temporal facts (e.g., events) in the future is crucial for many applications. The temporal facts in existing TKGs only contain their core entities (i.e., the entities playing core roles therein) and formulate them as quadruples, i.e., (subject entity, predicate, object entity, timestamp). This formulation oversimplifies temporal facts and inevitably causes information loss. Therefore, we propose to describe a temporal fact more accurately as an n-tuple, containing not only its predicate and core entities, but also its auxiliary entities, as well as the roles of all entities. By so doing, TKGs are augmented to N-tuple Temporal Knowledge Graphs (N-TKGs). To conduct reasoning over N-TKGs, we further propose N-tuple Evolutional Network (NE-Net). It recurrently learns the evolutional representations of entities and predicates in temporal facts at different timestamps in the history via modeling the relations among those entities and predicates. Based on the learned representations, reasoning tasks at future timestamps can be realized via task-specific decoders. Experiment results on two newly built datasets demonstrate the superiority of N-TKG and the effectiveness of NE-Net.

A Temporal Knowledge Graph (TKG) is a sequence of KGs with respective timestamps, which adopts quadruples in the form of (subject, relation, object, timestamp) to describe dynamic facts. TKG reasoning has facilitated many real-world applications via answering such queries as (query entity, query relation, ?, future timestamp) about future. This is actually a matching task between a query and candidate entities based on their historical structures, which reflect behavioral trends of the entities at different timestamps. In addition, recent KGs provide background knowledge of all the entities, which is also helpful for the matching. Thus, in this paper, we propose the Historical Structure Matching (HiSMatch) model. It applies two structure encoders to capture the semantic information contained in the historical structures of the query and candidate entities. Besides, it adopts another encoder to integrate the background knowledge into the model. TKG reasoning experiments on six benchmark datasets demonstrate the significant improvement of the proposed HiSMatch model, with up to 5.6% performance improvement in MRR, compared to the state-of-the-art baselines.