发表机构
King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对知识库补全，提出四个递进的逻辑忠实性标准并证明其蕴含关系，基于相对模型计数定义最强标准，实验表明现有嵌入模型排名准确但不忠实。
AI 中文摘要
知识图谱补全通过将观察到的三元组排在随机损坏的三元组之上进行评估，这会将每个未观察到的知识视为假。当被补全的对象是描述逻辑知识库而非普通图谱时，开放世界假设和演绎闭包使得这种做法不充分：相对于知识库，一个候选公理是被蕴含、矛盾还是未确定，而一个无法将逻辑上不可能的公理与合理的新的公理区分开的模型不仅不太准确，而且在语义上是不正确的。我们提出知识库补全模型在逻辑上忠实意味着什么，以及当前的嵌入模型是否忠实。我们定义了四个日益严格的标准层级：判别、逻辑可接受性、单调逻辑忠实性和概率逻辑忠实性，并证明它们构成严格蕴含链。我们将最强的标准基于相对模型计数$P(α\mid\mathcal{O}) = \\#(\mathcal{O}\cup\{α\})/\\#(\mathcal{O})$，该计数在其端点恢复三分法，并对未确定的公理进行排序。在$\mathcal{EL}$本体上评估知识图谱和逻辑几何嵌入模型，使用推理器生成的蕴含、矛盾和未确定的测试集，我们发现排名准确度并不蕴含逻辑忠实性，且所评估的模型均未在整个层级上忠实。代码可在https://github.com/bio-ontology-research-group/kbc获取。
英文摘要
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 $P(α\mid\mathcal{O}) = \#(\mathcal{O}\cup\{α\})/\#(\mathcal{O})$, 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.
CommentsAccepted at NeSy 2026
