Several approaches have been developed that generate embeddings for Description Logic ontologies and use these embeddings in machine learning. One approach of generating ontologies embeddings is by first embedding the ontologies into a graph structure, i.e., introducing a set of nodes and edges for named entities and logical axioms, and then applying a graph embedding to embed the graph in $\mathbb{R}^n$. Methods that embed ontologies in graphs (graph projections) have different formal properties related to the type of axioms they can utilize, whether the projections are invertible or not, and whether they can be applied to asserted axioms or their deductive closure. We analyze, qualitatively and quantitatively, several graph projection methods that have been used to embed ontologies, and we demonstrate the effect of the properties of graph projections on the performance of predicting axioms from ontology embeddings. We find that there are substantial differences between different projection methods, and both the projection of axioms into nodes and edges as well ontological choices in representing knowledge will impact the success of using ontology embeddings to predict axioms.

翻译：已有多种方法为描述逻辑本体生成嵌入，并将这些嵌入应用于机器学习。生成本体嵌入的一种方法是先将本体嵌入到图结构中，即为命名实体和逻辑公理引入一组节点和边，然后应用图嵌入方法将图嵌入到$\mathbb{R}^n$中。将本体嵌入到图的方法（图投影）具有不同的形式特性，这些特性涉及它们能利用的公理类型、投影是否可逆，以及这些方法是否适用于断言公理或其演绎闭包。我们定性和定量地分析了若干用于嵌入本体的图投影方法，并展示了图投影特性对从本体嵌入预测公理性能的影响。我们发现不同投影方法之间存在显著差异，公理向节点和边的投影方式以及知识表示的本体选择，均会影响利用本体嵌入预测公理的成功率。