BoxLitE: A Faithful Knowledge Base Embedding Based on Convex Optimization

2026-04-27

AI Summary

A key challenge in knowledge graph embedding lies in effectively integrating TBox ontological knowledge with ABox facts while preserving logical faithfulness. This work proposes BoxLitE, the first model to represent concepts as convex regions in vector space within the DL-Lite^H framework and formalize embedding learning as a convex optimization problem. The approach guarantees the existence of weakly faithful embeddings for any satisfiable knowledge base and provides theoretical assurance of logical consistency. By innovatively combining convex region representations, ontological semantics, and convex optimization, BoxLitE achieves a knowledge graph embedding method that balances expressive power with logical faithfulness.

Abstract

Knowledge base (KB) embeddings aim at combining the capability of classical knowledge graph embeddings to generalize the information present in facts, the ABox, with conceptual knowledge represented in an ontology language, the TBox. Several authors have recently explored the idea of mapping concepts to convex regions in a vector space. This is useful to represent hierarchies, typically present in TBoxes, since more general concepts can be mapped to larger regions, containing those regions associated with more specific concepts. However, the power of convexity is rarely leveraged during the actual learning tasks. Here, we introduce BoxLitE, a KB embedding model for DL-Lite$^{\mathcal{H}}$ that allows for convex optimization. We show that for any satisfiable DL-Lite$^{\mathcal{H}}$ KB, there is a BoxLitE embedding that is a weakly faithful model. As a proof of concept, we show how to formulate the KB embedding task as a convex optimization problem and how to obtain embeddings with such desirable faithfulness properties.

Problem

• knowledge base embedding
• convex optimization
• DL-Lite
• TBox
• faithfulness

Innovation

• convex optimization
• knowledge base embedding
• DL-Lite
• faithful representation
• convex regions