Many problems in data mining can be viewed as a special case of the problem of enumerating the closed elements of an independence system w.r.t. some specific closure operator. We consider a generalization of this problem to strongly accessible set systems and arbitrary closure operators. For this more general problem setting, the closed sets can be enumerated with polynomial delay if deciding membership in the set system and computing the closure operator can be solved in polynomial time. We discuss potential applications in graph mining.