OWL (Web Ontology Language) ontologies, which are able to represent both relational and type facts as standard knowledge graphs and complex domain knowledge in Description Logic (DL) axioms, are widely adopted in domains such as healthcare and bioinformatics. Inspired by the success of knowledge graph embeddings, embedding OWL ontologies has gained significant attention in recent years. Current methods primarily focus on learning embeddings for atomic concepts and roles, enabling the evaluation based on normalized axioms through specially designed score functions. However, they often neglect the embedding of complex concepts, making it difficult to infer with more intricate axioms. This limitation reduces their effectiveness in advanced reasoning tasks, such as Ontology Learning and ontology-mediated Query Answering. In this paper, we propose EL++-closed ontology embeddings which are able to represent any logical expressions in DL via composition. Furthermore, we develop TransBox, an effective EL++-closed ontology embedding method that can handle many-to-one, one-to-many and many-to-many relations. Our extensive experiments demonstrate that TransBox often achieves state-of-the-art performance across various real-world datasets for predicting complex axioms.

翻译：OWL（Web本体语言）本体能够将关系型事实和类型事实表示为标准知识图谱，并将复杂领域知识表达为描述逻辑（DL）公理，因此在医疗健康和生物信息学等领域得到广泛应用。受知识图谱嵌入成功的启发，OWL本体嵌入近年来受到显著关注。现有方法主要侧重于学习原子概念和角色的嵌入，通过专门设计的评分函数实现基于规范化公理的评估。然而，这些方法往往忽略复杂概念的嵌入，导致难以处理更复杂的公理推理。这一局限降低了其在高级推理任务（如本体学习和本体介导的查询应答）中的有效性。本文提出EL++封闭本体嵌入方法，能够通过组合运算表示描述逻辑中的任意逻辑表达式。进一步，我们开发了TransBox——一种能够处理多对一、一对多和多对多关系的有效EL++封闭本体嵌入方法。大量实验表明，TransBox在多个真实数据集上的复杂公理预测任务中均取得了先进的性能。