Description logic (DL) ontologies extend knowledge graphs (KGs) with conceptual information and logical background knowledge. In recent years, there has been growing interest in inductive reasoning techniques for such ontologies, which promise to complement classical deductive reasoning algorithms. Similar to KG completion, several existing approaches learn ontology embeddings in a latent space, while additionally ensuring that they faithfully capture the logical semantics of the underlying DL. However, they suffer from several shortcomings, mainly due to a limiting role representation. We propose Box$^2$EL, which represents both concepts and roles as boxes (i.e., axis-aligned hyperrectangles) and demonstrate how it overcomes the limitations of previous methods. We theoretically prove the soundness of our model and conduct an extensive experimental evaluation, achieving state-of-the-art results across a variety of datasets. As part of our evaluation, we introduce a novel benchmark for subsumption prediction involving both atomic and complex concepts.

翻译：描述逻辑本体通过概念信息和逻辑背景知识扩展了知识图谱。近年来，针对此类本体的归纳推理技术日益受到关注，有望补充经典演绎推理算法。与知识图谱补全类似，现有方法在隐空间中学习本体嵌入，同时确保其忠实捕获底层描述逻辑的逻辑语义。然而，这些方法因角色表示受限而存在若干缺陷。我们提出Box$^2$EL，将概念与角色均表示为盒（即轴对齐超矩形），并论证其如何克服先前方法的局限性。我们从理论上证明模型的可信性，并通过广泛实验评估在多个数据集上取得最先进结果。评估过程中，我们引入了涉及原子概念与复杂概念的新包含关系预测基准测试。