TGDK.2.3.2.pdf
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Strong Faithfulness for ELH Ontology Embeddings
Authors
Victor Lacerda 
,
Ana Ozaki ,
Ricardo Guimarães
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TGDK, Volume 2, Issue 3
Volume: TGDK, Volume 2
Journal: Transactions on Graph Data and Knowledge (TGDK) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2024-12-18 (Submission Date: 2024-04-24, Acceptance Date: 2024-10-23)
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Victor Lacerda, Ana Ozaki, and Ricardo Guimarães. Strong Faithfulness for ELH Ontology Embeddings. In Transactions on Graph Data and Knowledge (TGDK), Volume 2, Issue 3, pp. 2:1-2:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/TGDK.2.3.2
Abstract
Ontology embedding methods are powerful approaches to represent and reason over structured knowledge in various domains. One advantage of ontology embeddings over knowledge graph embeddings is their ability to capture and impose an underlying schema to which the model must conform. Despite advances, most current approaches do not guarantee that the resulting embedding respects the axioms the ontology entails. In this work, we formally prove that normalized ELH has the strong faithfulness property on convex geometric models, which means that there is an embedding that precisely captures the original ontology. We present a region-based geometric model for embedding normalized ELH ontologies into a continuous vector space. To prove strong faithfulness, our construction takes advantage of the fact that normalized ELH has a finite canonical model. We first prove the statement assuming (possibly) non-convex regions, allowing us to keep the required dimensions low. Then, we impose convexity on the regions and show the property still holds. Finally, we consider reasoning tasks on geometric models and analyze the complexity in the class of convex geometric models used for proving strong faithfulness.
Subject Classification
ACM Subject Classification
- Theory of computation → Description logics
Keywords
- Knowledge Graph Embeddings
- Ontologies
- Description Logic
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