Representation learning in the form of semantic embeddings has been successfully applied to a variety of tasks in natural language processing and knowledge graphs. Recently, there has been growing interest in developing similar methods for learning embeddings of entire ontologies. We propose Box$^2$EL, a novel method for representation learning of ontologies in the Description Logic EL++, which represents both concepts and roles as boxes (i.e. axis-aligned hyperrectangles), such that the logical structure of the ontology is preserved. We theoretically prove the soundness of our model and conduct an extensive empirical evaluation, in which we achieve state-of-the-art results in subsumption prediction, link prediction, and deductive reasoning. As part of our evaluation, we introduce a novel benchmark for evaluating EL++ embedding models on predicting subsumptions involving both atomic and complex concepts.

翻译：以语义嵌入形式进行的表示学习已成功应用于自然语言处理和知识图谱中的多种任务。近年来，针对完整本体嵌入的学习方法研究日益兴起。我们提出Box$^2$EL——一种面向描述逻辑EL++的本体表示学习方法，该方法将概念与角色均表示为箱体（即轴对齐的超矩形），从而保持本体的逻辑结构。我们从理论上证明了模型的可信性，并通过广泛实证评估，在包含预测、链接预测及演绎推理任务中取得了最先进成果。作为评估工作的一部分，我们引入了一个新型基准测试，用于评估EL++嵌入模型对涉及原子概念与复合概念的包含关系预测性能。