  Knowledge base completion (KBC) aims to automatically infer missing facts by
exploiting information already present in a knowledge base (KB). A promising
approach for KBC is to embed knowledge into latent spaces and make predictions
from learned embeddings. However, existing embedding models are subject to at
least one of the following limitations: (1) theoretical inexpressivity, (2)
lack of support for prominent inference patterns (e.g., hierarchies), (3) lack
of support for KBC over higher-arity relations, and (4) lack of support for
incorporating logical rules. Here, we propose a spatio-translational embedding
model, called BoxE, that simultaneously addresses all these limitations. BoxE
embeds entities as points, and relations as a set of hyper-rectangles (or
boxes), which spatially characterize basic logical properties. This seemingly
simple abstraction yields a fully expressive model offering a natural encoding
for many desired logical properties. BoxE can both capture and inject rules
from rich classes of rule languages, going well beyond individual inference
patterns. By design, BoxE naturally applies to higher-arity KBs. We conduct a
detailed experimental analysis, and show that BoxE achieves state-of-the-art
performance, both on benchmark knowledge graphs and on more general KBs, and we
empirically show the power of integrating logical rules.
