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.

本文提出了基于概念描述高维球表示的嵌入方法，利用本体的演绎闭包和不同类型的否定语句，改进了本体嵌入的知识库或本体补全任务。

利用负采样和逻辑闭包过滤增强几何本体嵌入的 EL++

Enhancing Geometric Ontology Embeddings for $\mathcal{EL}^{++}$ with  Negative Sampling and Deductive Closure Filtering

Recently, ontology embeddings representing entities in a low-dimensional
space have been proposed for ontology completion. However, the ontology
embeddings for concept subsumption prediction do not address the difficulties
of similar and isolated entities and fail to extract the global information of
annotation axioms from an ontology. In this paper, we propose a self-matching
training method for the two ontology embedding models: Inverted-index Matrix
Embedding (InME) and Co-occurrence Matrix Embedding (CoME). The two embeddings
capture the global and local information in annotation axioms by means of the
occurring locations of each word in a set of axioms and the co-occurrences of
words in each axiom. The self-matching training method increases the robustness
of the concept subsumption prediction when predicted superclasses are similar
to subclasses and are isolated to other entities in an ontology. Our evaluation
experiments show that the self-matching training method with InME outperforms
the existing ontology embeddings for the GO and FoodOn ontologies and that the
method with the concatenation of CoME and OWL2Vec* outperforms them for the
HeLiS ontology.

本文提出了一个自匹配训练方法，对本体嵌入模型进行训练，包括倒排索引矩阵嵌入（InME）和共现矩阵嵌入（CoME），以捕捉本体注释公理中的全局和局部信息。通过自匹配训练方法，在预测超类与子类相似且与本体中其他实体孤立的情况下，可以提高概念包含预测的鲁棒性。实验证实，在 GO 和 FoodOn 本体中，使用 InME 的自匹配训练方法优于现有的本体嵌入方法；而在 HeLiS 本体中，使用 CoME 和 OWL2Vec * 的连接方法优于其他方法。