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A Complete Classification of the Complexity and Rewritability of Ontology-Mediated Queries based on the Description Logic EL

2019-04-29 09:34:54
Carsten Lutz, Leif Sabellek

Abstract

We provide an ultimately fine-grained analysis of the data complexity and rewritability of ontology-mediated queries (OMQs) based on an EL ontology and a conjunctive query (CQ). Our main results are that every such OMQ is in AC0, NL-complete, or PTime-complete and that containment in NL coincides with rewritability into linear Datalog (whereas containment in AC0 coincides with rewritability into first-order logic). We establish natural characterizations of the three cases in terms of bounded depth and (un)bounded pathwidth, and show that every of the associated meta problems such as deciding wether a given OMQ is rewritable into linear Datalog is ExpTime-complete. We also give a way to construct linear Datalog rewritings when they exist and prove that there is no constant Datalog rewritings.

Abstract (translated)

我们最终对基于EL本体和联合查询(CQ)的本体中介查询(OMQ)的数据复杂性和可重写性进行了细粒度分析。我们的主要结果是,每个这样的OMQ都在AC0、NL complete或ptime complete中,并且NL中的包含与线性数据日志中的可重写性一致(而AC0中的包含与一阶逻辑中的可重写性一致)。我们根据有界深度和(非)有界路径宽度建立了这三种情况的自然特征,并证明了所有相关的元问题,如确定给定OMQ是否可重写为线性数据日志是exptime完成的。我们还给出了一种在线性数据记录重写存在时构造它们的方法,并证明了没有恒定的数据记录重写。

URL

https://arxiv.org/abs/1904.12533

PDF

https://arxiv.org/pdf/1904.12533.pdf


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