Ontologies contain rich knowledge within domain, which can be divided into two categories, namely extensional knowledge and intensional knowledge. Extensional knowledge provides information about the concrete instances that belong to specific concepts in the ontology, while intensional knowledge details inherent properties, characteristics, and semantic associations among concepts. However, existing ontology embedding approaches fail to take both extensional knowledge and intensional knowledge into fine consideration simultaneously. In this paper, we propose a novel ontology embedding approach named EIKE (Extensional and Intensional Knowledge Embedding) by representing ontologies in two spaces, called extensional space and intensional space. EIKE presents a unified framework for embedding instances, concepts and their relations in an ontology, applying a geometry-based method to model extensional knowledge and a pretrained language model to model intensional knowledge, which can capture both structure information and textual information. Experimental results show that EIKE significantly outperforms state-of-the-art methods in three datasets for both triple classification and link prediction, indicating that EIKE provides a more comprehensive and representative perspective of the domain.

翻译：本体包含领域内丰富的知识，这些知识可分为两类：外延知识与内涵知识。外延知识提供属于本体中特定概念的具体实例信息，而内涵知识则详细描述概念间的固有属性、特征及语义关联。然而，现有的本体嵌入方法未能同时细致考量外延知识与内涵知识。本文提出一种名为EIKE（外延与内涵知识嵌入）的新型本体嵌入方法，通过在外延空间与内涵空间两个空间中表示本体来实现。EIKE提供了一个统一框架，用于嵌入本体中的实例、概念及其关系，采用基于几何的方法建模外延知识，并利用预训练语言模型建模内涵知识，从而同时捕捉结构信息与文本信息。实验结果表明，在三个数据集的三元组分类和链接预测任务中，EIKE均显著优于现有先进方法，这表明EIKE能够提供更全面且更具代表性的领域知识视角。