The instances of some classes may be specified extensionally. That is, one can list all of the instances of the class by definition. For this case we say (= (all-instances C) (setof V_1 V_2 ... V_n)), where C is a class and the V_i are its instances.ALL-INSTANCES imposes a monotonic constraint. Any subclass of C cannot have any instances outside of the ALL-INSTANCES of C. Note that this is not indexical or modal: whether something is in all-instances is a property of the modeled world and does not depend on the facts currently stored in some knowledge base.
(<=> (All-Instances ?Class ?Set-Of-Instances) (And (Class ?Class) (Set ?Set-Of-Instances) (Forall (?Instance) (<=> (Member ?Instance ?Set-Of-Instances) (Instance-Of ?Instance ?Class)))))
No. Instance-of maps indivdual instances to classes, whereas all-instances maps classes to sets of instances.