Relation NTH-DOMAIN

• Defined in theory: Frame-ontology
• Source code: frame-ontology.lisp

Slots on this relation:

Documentation:

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.

Instance-Of: Relation

Arity: 3

Equivalence Axioms:

(<=> (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:

(Nth-Domain Nth-Domain 3 Class)

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

Other Related Axioms:

(Nth-Domain Projection 3 Class)

(Nth-Domain Projection 2 Positive-Integer)

(<=> (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))))))

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

(Nth-Domain All-Values 2 Binary-Relation)

(Nth-Domain Value-Type 3 Class)

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

(Nth-Domain Same-Values 3 Binary-Relation)

(Nth-Domain Same-Values 2 Binary-Relation)

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

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

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

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

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

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

(Nth-Domain Slot-Value-Type 3 Class)

(Nth-Domain Slot-Value-Type 2 Binary-Relation)

(Nth-Domain Slot-Value-Type 1 Class)

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

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

(Nth-Domain Slot-Cardinality 1 Class)

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

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

(Nth-Domain Minimum-Slot-Cardinality 1 Class)

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

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

(Nth-Domain Maximum-Slot-Cardinality 1 Class)

(Nth-Domain Inherited-Slot-Value 2 Binary-Relation)

(Nth-Domain Inherited-Slot-Value 1 Class)

(Nth-Domain All-Inherited-Slot-Values 2 Binary-Relation)

(Nth-Domain All-Inherited-Slot-Values 1 Class)

(Nth-Domain Same-Slot-Values 3 Binary-Relation)

(Nth-Domain Same-Slot-Values 2 Binary-Relation)

(Nth-Domain Same-Slot-Values 1 Class)

(Nth-Domain Inherited-Facet-Value 3 Binary-Relation)

(Nth-Domain Inherited-Facet-Value 2 Class)

Notes:

• 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.