We study the relative expressiveness of ontology-mediated queries (OMQs) formulated in the expressive Description Logic extended with closed predicates. In particular, we present a polynomial time translation from OMQs into Datalog with negation under the stable model semantics, the formalism that underlies Answer Set Programming. This is a novel and non-trivial result: the considered OMQs are not only non-monotonic, but also feature a tricky combination of nominals, inverse roles, and counting. We start with atomic queries and then lift our approach to a large class of first-order queries where quantification is “guarded” by closed predicates. Our translation is based on a characterization of the query answering problem via integer programming, and a specially crafted program in Datalog with negation that finds solutions to dynamically generated systems of integer inequalities. As an important by-product of our translation we get that the query answering problem is co-NP-complete in data complexity for the considered class of OMQs. Thus, answering these OMQs in the presence of closed predicates is not harder than answering them in the standard setting. This is not obvious as closed predicates are known to increase data complexity for some existing ontology languages.

中文翻译：

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具有封闭谓词的[公式省略]的数据记录可重写性和数据复杂性

我们研究以封闭谓词扩展的表达描述逻辑中表述的本体介导查询（OMQ）的相对表达能力。特别是，我们提出了在稳定模型语义下从 OMQ 到带有否定的 Datalog 的多项式时间转换，这是答案集编程基础的形式主义。这是一个新颖且重要的结果：所考虑的 OMQ 不仅是非单调的，而且还具有名义词、逆角色和计数的棘手组合。我们从原子查询开始，然后将我们的方法提升到一大类一阶查询，其中量化由封闭谓词“保护”。我们的翻译基于通过整数编程对查询回答问题的表征，以及 Datalog 中特制的带有否定的程序，该程序可以找到动态生成的整数不等式系统的解决方案。作为我们翻译的一个重要副产品，我们发现查询回答问题对于所考虑的 OMQ 类来说在数据复杂性上是共同 NP 完全的。因此，在存在封闭谓词的情况下回答这些 OMQ 并不比在标准设置中回答它们更难。这并不明显，因为已知封闭谓词会增加某些现有本体语言的数据复杂性。