  Ontologies often require knowledge representation on multiple levels of
abstraction, but description logics (DLs) are not well-equipped for supporting
this. We propose an extension of DLs in which abstraction levels are
first-class citizens and which provides explicit operators for the abstraction
and refinement of concepts and roles across multiple abstraction levels, based
on conjunctive queries. We prove that reasoning in the resulting family of DLs
is decidable while several seemingly harmless variations turn out to be
undecidable. We also pinpoint the precise complexity of our logics and several
relevant fragments.
