  This paper provides a model theoretic semantics to feature terms augmented
with set descriptions. We provide constraints to specify HPSG style set
descriptions, fixed cardinality set descriptions, set-membership constraints,
restricted universal role quantifications, set union, intersection, subset and
disjointness. A sound, complete and terminating consistency checking procedure
is provided to determine the consistency of any given term in the logic. It is
shown that determining consistency of terms is a NP-complete problem.
