The VALUE-CARDINALITY of a binary-relation with respect to a given domain instance is the number of range-elements to which the relation maps the domain-element. For a function (single-valued relation), the VALUE-CARDINALITY is 1 on all domain instances for which the function is defined. It is 0 for those instances outside the exact domain of the function.
VALUE-CARDINALITY may be used within the definition of a class to specify a slot cardinality if its first argument is the class's instance variable.
(Nth-Domain Value-Cardinality 3 Nonnegative-Integer) (Nth-Domain Value-Cardinality 2 Binary-Relation) (=> (Value-Cardinality ?Instance ?Binary-Relation ?N) (= ?N (Cardinality (Setofall ?Y (Holds ?Binary-Relation ?Instance ?Y)))))