Knowledge Base Embeddings: Semantics and Theoretical Properties
Camille Bourgaux, Ricardo Guimarães, Raoul Koudijs, Victor Lacerda, Ana Ozaki
TL;DR
Knowledge Base Embeddings extends KG embeddings to DL-based KBs (e.g., $ELHI_ot$, $ALC_p$) using region-based geometries, and introduces a formal semantic framework $S_M(E,L)$ to compare embedding methods along soundness, completeness, entailment closure, faithfulness, and expressiveness. It analyzes several methods (Convex Geometric, Cone-based al-cones, ELEm, ELBE, BoxEL, BoxE, ExpressivE) and shows that many do not simultaneously achieve all desirable properties; in finite DL languages many properties become equivalent. The study provides a principled lens for evaluating and guiding the design of KB embeddings with stronger theoretical guarantees, while highlighting core challenges such as encoding role disjointness and the bottom concept. It also suggests directions toward query-answering and explicit knowledge injection to broaden practical impact.
Abstract
Research on knowledge graph embeddings has recently evolved into knowledge base embeddings, where the goal is not only to map facts into vector spaces but also constrain the models so that they take into account the relevant conceptual knowledge available. This paper examines recent methods that have been proposed to embed knowledge bases in description logic into vector spaces through the lens of their geometric-based semantics. We identify several relevant theoretical properties, which we draw from the literature and sometimes generalize or unify. We then investigate how concrete embedding methods fit in this theoretical framework.