Machine learning with Semantic Web ontologies follows several strategies, one
of which involves projecting ontologies into graph structures and applying
graph embeddings or graph-based machine learning methods to the resulting
graphs. Several methods have been developed that project ontology axioms into
graphs. However, these methods are limited in the type of axioms they can
project (totality), whether they are invertible (injectivity), and how they
exploit semantic information. These limitations restrict the kind of tasks to
which they can be applied. Category-theoretical semantics of logic languages
formalizes interpretations using categories instead of sets, and categories
have a graph-like structure. We developed CatE, which uses the
category-theoretical formulation of the semantics of the Description Logic
$\mathcal{ALC}$ to generate a graph representation for ontology axioms. The
CatE projection is total and injective, and therefore overcomes limitations of
other graph-based ontology embedding methods which are generally not
invertible. We apply CatE to a number of different tasks, including deductive
and inductive reasoning, and we demonstrate that CatE improves over state of
the art ontology embedding methods. Furthermore, we show that CatE can also
outperform model-theoretic ontology embedding methods in machine learning tasks
in the biomedical domain.

本文提出了一种基于范畴论语义学的机器学习方法，使用 CatE 投影生成本体公理图表示，并应用于多种任务，展示了其超越了其他本体嵌入方法的局限性，并在生物医学领域的机器学习任务中优于现有的模型论本体嵌入方法。