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Strong Faithfulness for ELH Ontology Embeddings

Authors: Victor Lacerda, Ana Ozaki, and Ricardo Guimarães

Published in: TGDK, Volume 2, Issue 3 (2024). Transactions on Graph Data and Knowledge, Volume 2, Issue 3

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.

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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)

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@Article{lacerda_et_al:TGDK.2.3.2,
  author =	{Lacerda, Victor and Ozaki, Ana and Guimar\~{a}es, Ricardo},
  title =	{{Strong Faithfulness for ELH Ontology Embeddings}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{2:1--2:29},
  ISSN =	{2942-7517},
  year =	{2024},
  volume =	{2},
  number =	{3},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.2.3.2},
  URN =		{urn:nbn:de:0030-drops-225965},
  doi =		{10.4230/TGDK.2.3.2},
  annote =	{Keywords: Knowledge Graph Embeddings, Ontologies, Description Logic}
}

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Invited Paper

DOI: 10.4230/OASIcs.AIB.2022.2

Reasoning in Knowledge Graphs (Invited Paper)

Authors: Ricardo Guimarães and Ana Ozaki

Published in: OASIcs, Volume 99, International Research School in Artificial Intelligence in Bergen (AIB 2022)

Abstract

Knowledge Graphs (KGs) are becoming increasingly popular in the industry and academia. They can be represented as labelled graphs conveying structured knowledge in a domain of interest, where nodes and edges are enriched with metaknowledge such as time validity, provenance, language, among others. Once the data is structured as a labelled graph one can apply reasoning techniques to extract relevant and insightful information. We provide an overview of deductive and inductive reasoning approaches for reasoning in KGs.

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Ricardo Guimarães and Ana Ozaki. Reasoning in Knowledge Graphs (Invited Paper). In International Research School in Artificial Intelligence in Bergen (AIB 2022). Open Access Series in Informatics (OASIcs), Volume 99, pp. 2:1-2:31, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{guimaraes_et_al:OASIcs.AIB.2022.2,
  author =	{Guimar\~{a}es, Ricardo and Ozaki, Ana},
  title =	{{Reasoning in Knowledge Graphs}},
  booktitle =	{International Research School in Artificial Intelligence in Bergen (AIB 2022)},
  pages =	{2:1--2:31},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-228-0},
  ISSN =	{2190-6807},
  year =	{2022},
  volume =	{99},
  editor =	{Bourgaux, Camille and Ozaki, Ana and Pe\~{n}aloza, Rafael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.AIB.2022.2},
  URN =		{urn:nbn:de:0030-drops-160005},
  doi =		{10.4230/OASIcs.AIB.2022.2},
  annote =	{Keywords: Knowledge Graphs, Description Logics, Knowledge Graph Embeddings}
}

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Documents authored by Guimarães, Ricardo

Strong Faithfulness for ELH Ontology Embeddings

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Reasoning in Knowledge Graphs (Invited Paper)

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