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A hierarchy of faithfulness criteria for knowledge base completion

arXiv 2609.27863 ↗First posted 20 Aug 2026cs.AIcited by 0

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Abstract (arXiv)

Knowledge graph completion is evaluated by ranking observed triples above randomly corrupted ones, which treats every unobserved fact as false. When the object being completed is a description logic knowledge base rather than a plain graph, the open world assumption and deductive closure make this inadequate: relative to the knowledge base, a candidate axiom is entailed, contradictory, or undetermined, and a model that cannot separate a logically impossible axiom from a plausible novel one is not merely less accurate but semantically incorrect. We ask what it means for a knowledge base completion model to be logically faithful, and whether current embedding models are. We define a hierarchy of four increasingly strict criteria, discrimination, logical admissibility, monotonic logical faithfulness, and probabilistic logical faithfulness, and prove that they form a strict chain of implications. We ground the strongest criterion in the relative model count P(αmidO) = #(Ocupα)/#(O), which recovers the trichotomy at its endpoints and ranks undetermined axioms in between. Evaluating knowledge graph and logic-geometric embedding models on EL ontologies, with entailed, contradictory, and undetermined test sets generated by a reasoner, we find that ranking accuracy does not imply logical faithfulness and that none of the evaluated models is faithful across the hierarchy. The code is available at https://github.com/bio-ontology-research-group/kbc.

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References · 20

  1. 2014Embedding Entities and Relations for Learning and Inference in Knowledge Basescited by 932
  2. 2016Complex Embeddings for Simple Link Predictioncited by 902
  3. 2020Towards Faithfully Interpretable NLP Systems: How should we define and evaluate faithfulness?cited by 599
  4. 2019Neural Probabilistic Logic Programming in DeepProbLogcited by 394
  5. 2020Logic Tensor Networkscited by 199
  6. 2020Logical Neural Networkscited by 119
  7. 2020BoxE: A Box Embedding Model for Knowledge Base Completioncited by 105
  8. 2023Knowledge Graphs: Opportunities and Challengescited by 70
  9. 2017Knowledge Graph Embedding with Iterative Guidance from Soft Rulescited by 51
  10. 2019EL Embeddings: Geometric construction of models for the Description Logic EL ++cited by 48
  11. 2020Realistic Re-evaluation of Knowledge Graph Completion Methods: An Experimental Studycited by 37
  12. 2015Type-Constrained Representation Learning in Knowledge Graphscited by 34
8 more
  1. 2022Faithiful Embeddings for EL++ Knowledge Basescited by 25
  2. 2019Probability Calibration for Knowledge Graph Embedding Modelscited by 21
  3. 2023Dual Box Embeddings for the Description Logic EL++cited by 21
  4. 2018From Knowledge Graph Embedding to Ontology Embedding? An Analysis of the Compatibility between Vector Space Representations and Rulescited by 19
  5. 2022Rethinking Knowledge Graph Evaluation Under the Open-World Assumptioncited by 17
  6. 2022Description Logic EL++ Embeddings with Intersectional Closurecited by 16
  7. 2023Sem@K: Is my knowledge graph embedding model semantic-aware?cited by 10
  8. 2024Knowledge Base Embeddings: Semantics and Theoretical Propertiescited by 2

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