We study the problem of finite entailment of ontology-mediated queries. Going beyond local queries, we allow transitive closure over roles. We focus on ontologies formulated in the description logics ALCOI and ALCOQ, extended with transitive closure. For both logics, we show 2EXPTIME upper bounds for finite entailment of unions of conjunctive queries with transitive closure. We also provide a matching lower bound by showing that finite entailment of conjunctive queries with transitive closure in ALC is 2EXPTIME-hard.

中文翻译：

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关于描述逻辑中非局部查询的有限蕴涵

我们研究了本体中介查询的有限蕴涵问题。超越本地查询，我们允许对角色进行传递闭包。我们专注于描述逻辑 ALCOI 和 ALCOQ 中制定的本体，并通过传递闭包进行扩展。对于这两种逻辑，我们展示了具有传递闭包的联合查询的联合的有限蕴涵的 2EXPTIME 上限。我们还通过显示 ALC 中具有传递闭包的连接查询的有限蕴涵是 2EXPTIME-hard 来提供匹配的下限。