Ontology embeddings map classes, relations, and individuals in ontologies into $\mathbb{R}^n$, and within $\mathbb{R}^n$ similarity between entities can be computed or new axioms inferred. For ontologies in the Description Logic $\mathcal{EL}^{++}$, several embedding methods have been developed that explicitly generate models of an ontology. However, these methods suffer from some limitations; they do not distinguish between statements that are unprovable and provably false, and therefore they may use entailed statements as negatives. Furthermore, they do not utilize the deductive closure of an ontology to identify statements that are inferred but not asserted. We evaluated a set of embedding methods for $\mathcal{EL}^{++}$ ontologies based on high-dimensional ball representation of concept descriptions, incorporating several modifications that aim to make use of the ontology deductive closure. In particular, we designed novel negative losses that account both for the deductive closure and different types of negatives. We demonstrate that our embedding methods improve over the baseline ontology embedding in the task of knowledge base or ontology completion.

翻译：本体嵌入将本体中的类、关系和个体映射到$\mathbb{R}^n$空间中，在该空间中可计算实体间的相似度或推断新公理。针对描述逻辑$\mathcal{EL}^{++}$中的本体，目前已开发出若干显式生成本体模型的嵌入方法。然而，这些方法存在若干局限性：它们无法区分不可证明的陈述与可证明为假的陈述，因而可能将蕴含式陈述误用作负例；同时，它们未能利用本体的演绎闭包来识别可推断但未明确声明的陈述。我们评估了一系列基于概念描述的高维球表示的$\mathcal{EL}^{++}$本体嵌入方法，并引入了若干旨在利用本体演绎闭包的改进方案。特别地，我们设计了同时考虑演绎闭包与不同类型负例的新型负损失函数。实验表明，在知识库或本体补全任务中，我们的嵌入方法相较于基线本体嵌入模型取得了显著提升。