Such problems are that each relation R can be defined by a Boolean combination frequently intractable, but there are several important of equations over the signature,, andc, which are set CSPs that are known to be polynomial-time function symbols for intersection, union, and complementation, tractable. We introduce a large class of set CSPs respectively. Details of the formal definition and many that can be solved in quadratic time. Our class, examples of set constraint languages can be found in Section which we call EI, contains all previously known 3. The choice of N is just for notational convenience; tractable set CSPs, but also some new ones that as we will see, we could have selected any infinite set for are of crucial importance for example in description our purposes. In the following, a set constraint satisfaction logics. The class of EI set constraints has an problem (set CSP) is a problem of the form CSP(Γ) for a elegant universal-algebraic characterization, which set constraint language Γ. It has been shown by Marriott and we use to show that every set constraint language Odersky [Marriott and Odersky, 1996] that all set CSPs are that properly contains all EI set constraints already contained in NP; they also showed that the largest set constraint has a finite sublanguage with an NPhard constraint language, which consists of all relations that can be satisfaction problem.