The concept description formalisms of existing description logics syst
ems allow the user to express local cardinality restrictions on the fi
llers of a particular role. It is not possible, however, to introduce
global restrictions on the number of instances of a given concept. Thi
s article argues that such cardinality restrictions on concepts are of
importance in applications such as configuration of technical systems
, an application domain of description logics systems that is currentl
y gaining in interest, It shows that including such restrictions in th
e description language leaves the important inference problems such as
instance testing decidable. The algorithm combines and simplifies the
ideas developed for the treatment of qualified number restrictions an
d of general terminological axioms.