By Anonymous User
Review Details
Reviewer has chosen to be Anonymous
Overall Impression: Good
Content:
Technical Quality of the paper: Good
Originality of the paper: Yes
Adequacy of the bibliography: Yes
Presentation:
Adequacy of the abstract: Yes
Introduction: background and motivation: Good
Organization of the paper: Satisfactory
Level of English: Satisfactory
Overall presentation: Good
Detailed Comments:
This paper provides a rigorous theoretical analysis of box-based knowledge base embeddings for ELHO(○) ontologies. The central contribution is showing that Helly’s Property, an inherent geometric constraint of axis-aligned boxes, imposes unavoidable expressivity limitations on any box-based embedding method that uses standard assumptions (concepts as boxes, conjunction as intersection, etc.). As a consequence, some classically satisfiable ontologies cannot be represented by any such embedding, regardless of implementation details or learning procedures.
The paper develops the notions of Helly-satisfiability and Helly-faithfulness to characterize when an ontology can be modeled by a box interpretation and when geometric bias is unavoidable. It proposes a closure-based procedure to test Helly-satisfiability, introduces the idea of a Helly-companion ontology, and proves that Helly-satisfiable ontologies always admit finite Helly-closed models. These results offer a principled explanation for the incompleteness and lack of faithfulness observed in existing box-based KBE methods.
Strengths:
- The theoretical contribution is strong, general, and clearly relevant to ongoing work on neurosymbolic AI;
- The identification of HP as the fundamental obstacle to completeness/faithfulness is elegant and unifying across architectures;
- Formal definitions and proofs are well-structured and conceptually consistent;
- The results have practical implications for ontology engineering, link prediction, and diagnosing embedding failures;
- The work clarifies that these limitations are not tied to specific models but stem from geometry itself.
Weaknesses:
- The paper contains no empirical evaluation demonstrating how often real-world ontologies violate HP or how these violations manifest in trained models;
- The computational complexity of the Helly-satisfiability procedure is not well discussed, leaving its feasibility unclear.
- The discussion of alternative geometric frameworks (e.g., cones, general convex regions) is brief and could better situate the results;
- Some parts of the manuscript felt a bit redundant.
Overall, this is a solid and relevant theoretical paper that meaningfully analyzes the foundational limitations of box-based embeddings. While it would benefit from tightening some parts and adding more context on practical impact and alternatives, the core results are sound and significant.
