Understanding the Expressive Capabilities of Knowledge Base Embeddings under Box Semantics

Mena Leemhuis, Oliver Kutz

Keywords: Knowledge Base Embeddings, Boxes, Ontologies

TL;DR: This paper analyzes the expressive capabilities of box embeddings for $\mathcal{ELHO}(\circ)^\bot$ ontologies, indicates limitations based on Helly’s Property, and outlines a procedure to determine which ontologies can be correctly embedded.

Abstract: Knowledge base embeddings are a widely applied technique, used for instance to improve link prediction tasks on knowledge graphs by using the geometric regularities occurring during learning. Techniques where ontological concepts are interpreted as boxes have shown to be particularly useful in this context, as they are both suitably expressive and of low computational complexity. However, to use those regularities for learning, it is necessary to determine and understand the possible biases in the approach: how do we distinguish what is learned due to regularities in the data from what is simply based on the representational limitations of the embedding? In this paper, we establish that there are some severe limitations in expressivity when modeling description logic ontologies with box embeddings in intended target languages such as $\mathcal{ELHO}(\circ)^\bot$. We illustrate that, under some weak assumptions, box semantics always satisfy Helly's Property, and is thus too weak to capture semantically $\mathcal{ELHO}(\circ)^\bot$ in an adequate way. We then characterize how so-called Helly-satisfiable $\mathcal{ELHO}(\circ)^\bot$ ontologies can be adequately determined. We discuss the implications of this result with respect to existing box embedding approaches and real-world use cases.

Track: Knowledge Graphs, Ontologies and Neurosymbolic AI

Paper Type: Long Paper

Resubmission: No

Submission Number: 32