  We study FO-rewritability of conjunctive queries in the presence of
ontologies formulated in a description logic between EL and Horn-SHIF, along
with related query containment problems. Apart from providing
characterizations, we establish complexity results ranging from ExpTime via
NExpTime to 2ExpTime, pointing out several interesting effects. In particular,
FO-rewriting is more complex for conjunctive queries than for atomic queries
when inverse roles are present, but not otherwise.
