  Rewriting-based approaches for answering queries over an OWL 2 DL ontology
have so far been developed mainly for Horn fragments of OWL 2 DL. In this
paper, we study the possibilities of answering queries over non-Horn ontologies
using datalog rewritings. We prove that this is impossible in general even for
very simple ontology languages, and even if PTIME = NP. Furthermore, we present
a resolution-based procedure for $\SHI$ ontologies that, in case it terminates,
produces a datalog rewriting of the ontology. Our procedure necessarily
terminates on DL-Lite_{bool}^H ontologies---an extension of OWL 2 QL with
transitive roles and Boolean connectives.
