Query Rewriting Beyond DL-Lite.

Query rewriting has become a very prominent tool for efficiently implementing ontology-mediated querying in practice. The technique was originally introduced in the context of DL-Lite [4], but is now increasingly being used also for more expressive DLs. While rewritings are not guaranteed to exist beyond DL-Lite, the simple structure of ontologies that emerge from practical applications gives hope that non-existence of rewritings is a rare case. The aim of the talk is to survey FOand Datalog-rewriting of ontologymediated queries in description logics beyond DL-Lite. It is structured into three parts. The first part is concerned with FO-rewritings in Horn-DLs such as EL, ELI, and Horn-SHI, the second part considers FO-rewritings in non-Horn-DLs such as ALC and ALCI, and the third part is about Datalog-rewritings in nonHorn DLs. In all three parts, I will try to emphasize useful characterizations of FO-rewritability, practically efficient algorithms for constructing rewritings, and relevant computational complexity results. The presentation is based on joint work with Meghyn Bienvenu, Balder ten Cate, Peter Hansen, Inanc Seylan, and Frank Wolter. The subsequent section provides some supplementary material that is featured in the talk, but has not yet been published elsewhere. It establishes a link between the first and the second part of the talk.