N-ary Knowledge Graphs (NKGs), where a fact can involve more than two entities, have gained increasing attention. Link Prediction in NKGs (LPN) aims to predict missing elements in facts to facilitate the completion of NKGs. Current LPN methods implicitly operate under a closed-world assumption, meaning that the sets of entities and roles are fixed. These methods focus on predicting missing elements within facts composed of entities and roles seen during training. However, in reality, new facts involving unseen entities and roles frequently emerge, requiring completing these facts. Thus, this paper proposes a new task, Inductive Link Prediction in NKGs (ILPN), which aims to predict missing elements in facts involving unseen entities and roles in emerging NKGs. To address this task, we propose a Meta-learning-based N-ary knowledge Inductive Reasoner (MetaNIR), which employs a graph neural network with meta-learning mechanisms to embed unseen entities and roles adaptively. The obtained embeddings are used to predict missing elements in facts involving unseen elements. Since no existing dataset supports this task, three datasets are constructed to evaluate the effectiveness of MetaNIR. Extensive experimental results demonstrate that MetaNIR consistently outperforms representative models across all datasets.

Hyper-relational facts, which consist of a primary triple (head entity, relation, tail entity) and auxiliary attribute-value pairs, are widely present in real-world Knowledge Graphs (KGs). Link Prediction on Hyper-relational Facts (LPHFs) is to predict a missing element in a hyper-relational fact, which helps populate and enrich KGs. However, existing LPHFs studies usually require an amount of high-quality data. They overlook few-shot relations, which have limited instances, yet are common in real-world scenarios. Thus, we introduce a new task, Few-Shot Link Prediction on Hyper-relational Facts (FSLPHFs). It aims to predict a missing entity in a hyper-relational fact with limited support instances. To tackle FSLPHFs, we propose MetaRH, a model that learns Meta Relational information in Hyper-relational facts. MetaRH comprises three modules: relation learning, support-specific adjustment, and query inference. By capturing meta relational information from limited support instances, MetaRH can accurately predict the missing entity in a query. As there is no existing dataset available for this new task, we construct three datasets to validate the effectiveness of MetaRH. Experimental results on these datasets demonstrate that MetaRH significantly outperforms existing representative models.