We characterize the expressive power of description logic (DL) TBoxes, both for expressive DLs such as ALL and ALL QIO and lightweight DLs such as DL-Lite and ε£. Our characterizations are relative to first-order logic, based on a wide range of semantic notions such as bisimulation, equisim-ulation, 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.
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