The problem arises when we use a set whose completion is not over yet in the formation of another set, or even in its own formation. Then we are led to the question when the collection of all individuals satisfying an expression can be considered an individual itself. Since we are talking about the individuals as entities formed out of previously formed entities, the notion of cumulative hierarchy immediately comes to mind. This provides talking about collections of previously formed objects as a new object in a safe manner and prevents entities of very large size to be formed. At this point, the problem of sets which can be members of themselves arises, since such sets are used in their own formation.
Circularity is obviously a common means of commonsense knowledge representation.
Thus we conclude that a possible commonsense set theory should also allow circular sets to be expressed. However, such formalizations which also capture the cumulative hierarchy principle are not very common. Among theories revised so far, Aczel's theory is the only one which allows circularity. By proposing his Anti-Foundation Axiom, Aczel overrode the FA of ZF which prohibits circular sets, but preserved the hierarchical nature of the original axiomatization. Situations are parts of the reality that can enter into relations with other parts.