In a hyper-relational knowledge graph (HKG), each fact is composed of a main triple associated with attribute-value qualifiers, which express additional factual knowledge. The hyper-relational knowledge graph completion (HKGC) task aims at inferring plausible missing links in a HKG. Most existing approaches to HKGC focus on enhancing the communication between qualifier pairs and main triples, while overlooking two important properties that emerge from the monotonicity of the hyper-relational graphs representation regime. Stage Reasoning allows for a two-step reasoning process, facilitating the integration of coarse-grained inference results derived solely from main triples and fine-grained inference results obtained from hyper-relational facts with qualifiers. In the initial stage, coarse-grained results provide an upper bound for correct predictions, which are subsequently refined in the fine-grained step. More generally, Qualifier Monotonicity implies that by attaching more qualifier pairs to a main triple, we may only narrow down the answer set, but never enlarge it. This paper proposes the HyperMono model for hyper-relational knowledge graph completion, which realizes stage reasoning and qualifier monotonicity. To implement qualifier monotonicity HyperMono resorts to cone embeddings. Experiments on three real-world datasets with three different scenario conditions demonstrate the strong performance of HyperMono when compared to the SoTA.

Extracting hyper-relations is crucial for constructing comprehensive knowledge graphs, but there are limited supervised methods available for this task. To address this gap, we introduce a zero-shot prompt-based method using OpenAI's GPT-3.5 model for extracting hyper-relational knowledge from text. Comparing our model with a baseline, we achieved promising results, with a recall of 0.77. Although our precision is currently lower, a detailed analysis of the model outputs has uncovered potential pathways for future research in this area.

A hyper-relational knowledge graph has been recently studied where a triplet is associated with a set of qualifiers; a qualifier is composed of a relation and an entity, providing auxiliary information for a triplet. While existing hyper-relational knowledge graph embedding methods assume that the entities are discrete objects, some information should be represented using numeric values, e.g., (J.R.R., was born in, 1892). Also, a triplet (J.R.R., educated at, Oxford Univ.) can be associated with a qualifier such as (start time, 1911). In this paper, we propose a unified framework named HyNT that learns representations of a hyper-relational knowledge graph containing numeric literals in either triplets or qualifiers. We define a context transformer and a prediction transformer to learn the representations based not only on the correlations between a triplet and its qualifiers but also on the numeric information. By learning compact representations of triplets and qualifiers and feeding them into the transformers, we reduce the computation cost of using transformers. Using HyNT, we can predict missing numeric values in addition to missing entities or relations in a hyper-relational knowledge graph. Experimental results show that HyNT significantly outperforms state-of-the-art methods on real-world datasets.

Link Prediction on Hyper-relational Knowledge Graphs (HKG) is a worthwhile endeavor. HKG consists of hyper-relational facts (H-Facts), composed of a main triple and several auxiliary attribute-value qualifiers, which can effectively represent factually comprehensive information. The internal structure of HKG can be represented as a hypergraph-based representation globally and a semantic sequence-based representation locally. However, existing research seldom simultaneously models the graphical and sequential structure of HKGs, limiting HKGs' representation. To overcome this limitation, we propose a novel Hierarchical Attention model for HKG Embedding (HAHE), including global-level and local-level attention. The global-level attention can model the graphical structure of HKG using hypergraph dual-attention layers, while the local-level attention can learn the sequential structure inside H-Facts via heterogeneous self-attention layers. Experiment results indicate that HAHE achieves state-of-the-art performance in link prediction tasks on HKG standard datasets. In addition, HAHE addresses the issue of HKG multi-position prediction for the first time, increasing the applicability of the HKG link prediction task. Our code is publicly available.

Complex query answering (CQA) is an essential task for multi-hop and logical reasoning on knowledge graphs (KGs). Currently, most approaches are limited to queries among binary relational facts and pay less attention to n-ary facts (n>=2) containing more than two entities, which are more prevalent in the real world. Moreover, previous CQA methods can only make predictions for a few given types of queries and cannot be flexibly extended to more complex logical queries, which significantly limits their applications. To overcome these challenges, in this work, we propose a novel N-ary Query Embedding (NQE) model for CQA over hyper-relational knowledge graphs (HKGs), which include massive n-ary facts. The NQE utilizes a dual-heterogeneous Transformer encoder and fuzzy logic theory to satisfy all n-ary FOL queries, including existential quantifiers, conjunction, disjunction, and negation. We also propose a parallel processing algorithm that can train or predict arbitrary n-ary FOL queries in a single batch, regardless of the kind of each query, with good flexibility and extensibility. In addition, we generate a new CQA dataset WD50K-NFOL, including diverse n-ary FOL queries over WD50K. Experimental results on WD50K-NFOL and other standard CQA datasets show that NQE is the state-of-the-art CQA method over HKGs with good generalization capability. Our code and dataset are publicly available.

Multi-hop logical reasoning is an established problem in the field of representation learning on knowledge graphs (KGs). It subsumes both one-hop link prediction as well as other more complex types of logical queries. Existing algorithms operate only on classical, triple-based graphs, whereas modern KGs often employ a hyper-relational modeling paradigm. In this paradigm, typed edges may have several key-value pairs known as qualifiers that provide fine-grained context for facts. In queries, this context modifies the meaning of relations, and usually reduces the answer set. Hyper-relational queries are often observed in real-world KG applications, and existing approaches for approximate query answering cannot make use of qualifier pairs. In this work, we bridge this gap and extend the multi-hop reasoning problem to hyper-relational KGs allowing to tackle this new type of complex queries. Building upon recent advancements in Graph Neural Networks and query embedding techniques, we study how to embed and answer hyper-relational conjunctive queries. Besides that, we propose a method to answer such queries and demonstrate in our experiments that qualifiers improve query answering on a diverse set of query patterns.