  For many years, link prediction on knowledge graphs (KGs) has been a purely
transductive task, not allowing for reasoning on unseen entities. Recently,
increasing efforts are put into exploring semi- and fully inductive scenarios,
enabling inference over unseen and emerging entities. Still, all these
approaches only consider triple-based \glspl{kg}, whereas their richer
counterparts, hyper-relational KGs (e.g., Wikidata), have not yet been properly
studied. In this work, we classify different inductive settings and study the
benefits of employing hyper-relational KGs on a wide range of semi- and fully
inductive link prediction tasks powered by recent advancements in graph neural
networks. Our experiments on a novel set of benchmarks show that qualifiers
over typed edges can lead to performance improvements of 6% of absolute gains
(for the Hits@10 metric) compared to triple-only baselines. Our code is
available at \url{https://github.com/mali-git/hyper_relational_ilp}.
