Underdetermined sets is a new type of data structures (terms) developed in Actor Prolog . ... The point is that an underdetermined set can include some indefinite rest (a tail) like a list in usual Prolog . At the same time, the order of elements of an underdetermined set can be arbitrary one and it does not affect results of unification of underdetermined sets. Moreover, Actor Prolog guarantees that a rest of an underdetermined set never contains elements that are explicitly given in the set. ...