  We characterize the expressive power of description logic (DL) TBoxes, both
for expressive DLs such as ALC and ALCQIO and lightweight DLs such as DL-Lite
and EL. Our characterizations are relative to first-order logic, based on a
wide range of semantic notions such as bisimulation, equisimulation, disjoint
union, and direct product. We exemplify the use of the characterizations by a
first study of the following novel family of decision problems: given a TBox T
formulated in a DL L, decide whether T can be equivalently rewritten as a TBox
in the fragment L' of L.
