  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.
