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：以语义嵌入为形式的表示学习已成功应用于自然语言处理和知识图谱中的各类任务。近年来，针对整个本体进行嵌入学习方法的研究日益受到关注。我们提出Box$^2$EL，一种新颖的描述逻辑EL++本体表示学习方法，该方法将概念与角色均表示为盒（即轴对齐超矩形），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，并开展了广泛的实证评估，在包含预测、链接预测和演绎推理任务中取得了最先进的成果。作为评估的一部分，我们引入了一个新型基准测试集，用于评估EL++嵌入模型在涉及原子概念与复杂概念的包含关系预测性能。