SHACL and OWL are two prominent W3C standards for managing RDF data. These languages share many features, but they have one fundamental difference: OWL, designed for inferring facts from incomplete data, makes the open-world assumption, whereas SHACL is a constraint language that treats the data as complete and must be validated under the closed-world assumption. The combination of both formalisms is very appealing and has been called for, but their semantic gap is a major challenge, semantically and computationally. In this paper, we advocate a semantics for SHACL validation in the presence of ontologies based on core universal models. We provide a technique for constructing these models for ontologies in the rich data-tractable description logic Horn-ALCHIQ. Furthermore, we use a finite representation of this model to develop a rewriting technique that reduces SHACL validation in the presence of ontologies to standard validation. Finally, we study the complexity of SHACL validation in the presence of ontologies, and show that even very simple ontologies make the problem EXPTIME-complete, and PTIME-complete in data complexity.

翻译：SHACL与OWL是W3C制定的两个重要RDF数据管理标准。这两种语言共享诸多特性，但存在一个根本差异：OWL专为从不完整数据中推导事实而设计，采用开放世界假设；而SHACL作为约束语言，将数据视为完整集合，必须在封闭世界假设下进行验证。两种形式化方法的结合极具吸引力且备受期待，但其语义鸿沟在语义层面和计算层面均构成重大挑战。本文提出一种基于核心通用模型的、支持本体存在的SHACL验证语义。我们为表达能力丰富且数据易处理的描述逻辑Horn-ALCHIQ中的本体，提供了构建此类模型的技术。此外，我们利用该模型的有限表示形式，开发出一种重写技术，将存在本体情况下的SHACL验证问题转化为标准验证问题。最后，我们研究了存在本体情况下SHACL验证的计算复杂度，证明即使是非常简单的本体也会使该问题成为EXPTIME完全问题，而在数据复杂度层面为PTIME完全问题。