This paper provides a model theoretic semantics to fea- ture terms augmented with set descriptions. We pro- vide constraints to specify HPSG style set descriptions, fixed cardinality set descriptions, set-membership con- straints, restricted universal role quantifications, set union, intersection, subset and disjointness. A sound, complete and terminating consistency checking proce- dure 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.

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