Relation Range

Arity: 2
Definition-Sort-Index@Interface-Ontology: 100
RANGE is short for ``range restriction.'' Specifying a RANGE restriction of a relation is a way to constrain the class of objects which participate as the last argument to the relation. For any tuple <d1 d2 ...dn r> in the relation, if class T is a RANGE restriction of the relation, r must be an instance of T.

RANGE restrictions are very helpful in maintaining ontologies. One can think of a range restriction as a type constraint on the value of a function or range of a relation. Representation systems can use these specifications to classify terms and check integrity constraints.

If the restriction on the range of the relation is not captured by a named class, one can use specify the constraint with a predicate that defines the class implicitly, coerced into a class. For example, (kappa (?x) (and (prime ?x) (< ?x 100)))
denotes the class of prime numbers under 100.

It is consistent to specify more than one RANGE restriction for a relation, as long as they all include the EXACT-RANGE of the relation.

Note that range restriction is true regardless of what the restricted relation is applied to. For class-specific range constraints, use slot-value-type.


Domain: Relation
Binary-Relation, Binary-Relation, Relation, Relation, Relation ...
Inverse: Range-Of
Range: Class

Implication Axioms for Range:

(=> (Range ?Relation ?Type)
    (Subclass-Of (Exact-Range ?Relation) ?Type))

Equivalence Axioms for Range:

(<=> (Range ?Relation ?Type)
     (And (Relation ?Relation)
          (Class ?Type)
          (Subclass-Of (Exact-Range ?Relation) ?Type)))

Axioms for Range:

(Relation ?Relation)

Frame References to Range:

In function Cardinality:

Range: Integer

In relation Domain:

Range: Class

In function Arity:

Range: Integer

In function Float-Digits:

Range: Nonnegative-Integer

In function Integer-Length:

Range: Nonnegative-Integer

In relation Subclass-Partition:

Range: Class-Partition