Abstract
We investigate the decidability and computational
complexity of query conservative extensions in Horn
description logics (DLs) with inverse roles. This is
more challenging than without inverse roles because
characterizations in terms of unbounded homomorphisms between universal models fail, blocking the standard approach to establishing decidability. We resort to a combination of automata
and mosaic techniques, proving that the problem is
2EXPTIME-complete in Horn-ALCHIF (and also
in Horn-ALC and in ELI). We obtain the same upper bound for deductive conservative extensions, for
which we also prove a CONEXPTIME lower bound