Conjunctive Query Answering for Expressive Description Logics

智能系统通常使用基于逻辑的数据和知识表示形式来实现。与传统数据库相比，这具有多方面的优势。例如，可以用灵活的模式来表示不同结构的信息。此外，这样的系统具有这样的好处，即所表示的知识中的逻辑隐含的结论可以通过推理算法自动导出。一个非常重要的推理服务是回答合取查询，它也构成了在语义Web领域广泛使用的SPARQL查询语言的基础。知识表示形式通常基于描述逻辑(例如，OWL)，描述逻辑是一阶逻辑的一族可判定片段。然而，到目前为止，还没有实际可用的技术来回答具有表达能力的描述逻辑的合取查询。然而，这种逻辑在实际中经常被使用，因为它们提供了更多的建模构造器，因此，它们允许更详细地表示知识和数据。在这个项目中，我们提出了一种新的技术，用非常有表现力的描述逻辑来回答合取查询。该方法基于深度集成到推理过程中，其中合取查询被转换(吸收)为基于规则的公理，这些公理直接由专门的推理算法处理。相比之下，现有的方法使用推理系统作为黑盒，将查询回答简化为标准的推理服务。直接和深入的集成还允许进行更复杂的优化，因此，有望提供更好的性能来回答合取查询。此外，表示知识中逻辑隐含但没有显式陈述的个体可以被认为是有效的，即计算所有逻辑隐含的答案在实践中变得可行。为了吸收查询，我们计划使用所谓的名义模式，我们在最近的前期工作中为其开发了高效的推理算法。首先，我们计划将使用名义模式的吸收扩展到合取查询，这样得到的基于规则的表达式可以通过适当扩展的推理过程来处理。其次，我们计划从理论上和实践上分析该方法可以应用于哪些语言片段。第三，我们计划开发和实现特定的优化，以便该技术可以受益于更深入地集成到推理过程中，并能很好地扩展到更大量的数据。最后，我们计划用现有的技术对我们的新的合取查询回答方法进行实证评估，该项目显著提高了更具表现力的描述逻辑的实际可用性，从而允许在实际的信息系统中对数据和知识进行更详细的建模和表示。

Intelligent systems are often realised with logic-based data and knowledge representation formalisms. This has various advantages in comparison to classical databases. For example, it is possible to represent inhomogeneously structured information with a flexible schema. Moreover, such systems have the benefit that logically implied conclusions in the represented knowledge can automatically be derived by reasoning algorithms. A very important reasoning service is answering conjunctive queries, which constitutes also the basis of the SPARQL query language that is widely used in the area of the Semantic Web. The knowledge representation formalism is often based on Description Logics (e.g., OWL), which is a family of decidable fragments of First Order Logics. So far, there exist, however, no practically usable techniques for answering conjunctive queries with expressive Description Logics. Nevertheless, such logics are often used in practice since they provide more modelling constructors and, therefore, they allow for representing knowledge and data in more detail.With this project, we propose a novel technique for conjunctive query answering with very expressive Description Logics. The approach is based on a deep integration into reasoning procedures, where the conjunctive queries are transformed (absorbed) into rule-based axioms, which are directly handled by specialised reasoning algorithms. In contrast, existing approaches use reasoning systems as black-boxes and reduce query answering to standard reasoning services. The direct and deep integration also allows for more sophisticated optimisations and, therefore, promises a much better performance for answering conjunctive queries. Furthermore, logically implied but not explicitly stated individuals in the represented knowledge can be considered efficiently, i.e., computing all logically implied answers becomes feasible in practice.For absorbing the queries, we plan to use so-called nominal schemas, for which we developed efficient reasoning algorithms in our recent preliminary work. First, we plan to extend absorption using nominal schemas to conjunctive queries in such a way that the resulting rule-based expressions can be handled by suitably extended reasoning procedures. Second, we plan to analyse theoretically as well as practically for which language fragments the approach can be applied. Third, we plan to develop and realise specific optimisations such that the technique can benefit from the deeper integration into the reasoning procedure and scales well to larger amounts of data. Last but not least, we plan to empirically evaluate our novel conjunctive query answering approach with existing techniques.The proposed project significantly improves the practical usability of more expressive Description Logics, which allows for a more detailed modelling and representation of data and knowledge in practical information systems.