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性并推断新公理。针对描述逻辑$\mathcal{EL}^{++}$的本体，已有若干嵌入方法能显式生成本体的模型。然而这些方法存在局限性：它们无法区分不可证明与可证伪的陈述，因此可能将蕴含语句用作负例。此外，它们未利用本体的演绎闭包来识别被推断而非断言的陈述。本研究评估了一组基于概念描述高维球体表示的$\mathcal{EL}^{++}$本体嵌入方法，并引入若干旨在利用本体演绎闭包的改进措施。特别地，我们设计了兼顾演绎闭包与不同类型负例的新型负损失函数。实验表明，我们的嵌入方法在知识库或本体补全任务中的性能优于基准本体嵌入方法。