Class Role-Class

Notes for Role-Class:

Slots on class Role-Class:

Arity: 1
A special kind of Class which is defined as the set of all Entities playing a particular Role in some Relation.

To the extent that updates may occur which change the particular set of tuples comprising a relation, being an instance of such a class is dynamically determined.

Has-Instance: Qua-Entity
Instance-Of: Class, Relation, Set
Subclass-Of: Class, Relation, Set

Slots on instances of Role-Class:

Arity: 1

Equivalence Axioms for Role-Class:

(<=> (Role-Class ?X)
     (Exists (?R ?N)
             (And (Relation ?R)
                  (Natural ?N)
                  (Forall (?Z)
                          (<=> (Instance-Of ?Z ?X)
                               (Exists (?Args)
                                       (And (List ?Args)
                                            (Holds ?R ?Args)
                                            (= (Nth ?Args ?N) ?Z))))))))

Other Related Equivalence Axioms for Role-Class:

(<=> (Qua-Entity ?X)
     (Exists (?Rc) (And (Role-Class ?Rc) (Instance-Of ?X ?Rc))))