  We introduce and investigate the expressive description logic (DL) ALCSCC++,
in which the global and local cardinality constraints introduced in previous
papers can be mixed. On the one hand, we prove that this does not increase the
complexity of satisfiability checking and other standard inference problems. On
the other hand, the satisfiability problem becomes undecidable if inverse roles
are added to the languages. In addition, even without inverse roles,
conjunctive query entailment in this DL turns out to be undecidable. We prove
that decidability of querying can be regained if global and local constraints
are not mixed and the global constraints are appropriately restricted. The
latter result is based on a locally-acyclic model construction, and it reduces
query entailment to ABox consistency in the restricted setting, i.e., to ABox
consistency w.r.t. restricted cardinality constraints in ALCSCC, for which we
can show an ExpTime upper bound.
