Relation Nth-Domain

Arity: 3
Domain restrictions generalized to n-ary relations. The sentence (nth-domain rel 3 type-class) says that the 3rd element of each tuple in the relation REL is an instance of type-class.


  • What about nth-range?

    A range restriction of a function is the same thing as an nth-domain restriction on the last element of each tuple, i.e., the values of the function. Therefore there is no nth-range relation.

Instance-Of: Relation, Set

Implication Axioms for Nth-Domain:

(=> (Nth-Domain ?Relation ?N ?Type)
    (Forall (?Tuple)
            (=> (Member ?Tuple ?Relation)
                (And (>= (Length ?Tuple) ?N)
                     (Instance-Of (Nth ?Tuple ?N) ?Type)))))

Equivalence Axioms for Nth-Domain:

(<=> (Nth-Domain ?Relation ?N ?Type)
     (And (Defined (Arity ?Relation))
          (Positive-Integer ?N)
          (Class ?Type)
          (Forall (?Tuple)
                  (=> (Member ?Tuple ?Relation)
                      (And (>= (Length ?Tuple) ?N)
                           (Instance-Of (Nth ?Tuple ?N) ?Type))))))

Axioms for Nth-Domain:

(Positive-Integer ?N)

(Defined (Arity ?Relation))

(Nth-Domain Nth-Domain 3 Class)

(Nth-Domain Nth-Domain 2 Positive-Integer)

Axioms mentioning Nth-Domain:

(Nth-Domain Value-Cardinality 3 Nonnegative-Integer)

(Nth-Domain Value-Cardinality 2 Binary-Relation)

(Nth-Domain Slot-Cardinality 3 Nonnegative-Integer)

(Nth-Domain Slot-Cardinality 2 Binary-Relation)

(Nth-Domain Slot-Cardinality 1 Class)