A hierarchy of faithfulness criteria for knowledge base completion

来源摘要

arXiv:2609.27863v1 Announce Type: new Abstract: 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 $P(\alpha\mid\mathcal{O}) = \#(\mathcal{O}\cup\{\alpha\})/\#(\mathcal{O})$, which recovers the trichotomy at its endpoints and ranks undetermined axioms in between. Evaluating knowledge graph and logic-geometric embedding models on $\mathcal{EL}$ 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.