Ontologies often require knowledge representation on multiple levels of abstraction, but description logics (DLs) are not well-equipped for supporting this. We propose an extension of DLs in which abstraction levels are first-class citizens and which provides explicit operators for the abstraction and refinement of concepts and roles across multiple abstraction levels, based on conjunctive queries. We prove that reasoning in the resulting family of DLs is decidable while several seemingly harmless variations turn out to be undecidable. We also pinpoint the precise complexity of our logics and several relevant fragments.

翻译：本体通常需要在多个抽象层级上进行知识表示，但描述逻辑对此支持不足。我们提出一种描述逻辑的扩展，其中抽象层级成为一等公民，并基于合取查询提供用于跨多个抽象层级对概念和角色进行抽象与精化的显式算子。我们证明：所得描述逻辑家族中的推理是可判定的，而若干看似无害的变体却不可判定。我们还精确标定了所提出逻辑及其若干相关片段的具体复杂度。