A term is defined if it does not denote the undefined object, called bottom. (defined (F x)) means that the function F is defined for the object x. (F x) denotes its value. In relational terminology, (defined (F x)) means (exists ?y (F x ?y)).Notes:
- DEFINED is not in the KIF 3.0 spec.
(<=> (Defined ?X) (Not (Undefined ?X)))
(=> (= (Projection@Frame-Ontology ?Relation ?Column) ?Projection-Relation) (Defined (Arity@Frame-Ontology ?Relation))) (=> (Subrelation-Of@Frame-Ontology ?Child-Relation ?Parent-Relation) (=> (Defined (Arity@Frame-Ontology ?Parent-Relation)) (= (Arity@Frame-Ontology ?Child-Relation) (Arity@Frame-Ontology ?Parent-Relation))))
(<=> (Projection@Frame-Ontology ?Relation ?Column) (And (Defined (Arity@Frame-Ontology ?Relation)) (Positive-Integer ?Column) (=< ?Column (Arity@Frame-Ontology ?Relation)) (Class@Frame-Ontology ?Projection-Relation) (Forall (?Projection-Instance) (<=> (Instance-Of@Frame-Ontology ?Instance ?Projection-Relation) (Exists (?Tuple) (And (Member ?Tuple ?Relation) (= (Nth ?Tuple ?Column) ?Instance))))))) (<=> (Nth-Domain@Frame-Ontology ?Relation ?N ?Type) (And (Defined (Arity@Frame-Ontology ?Relation)) (Positive-Integer ?N) (Class@Frame-Ontology ?Type) (Forall (?Tuple) (=> (Member ?Tuple ?Relation) (And (>= (Length ?Tuple) ?N) (Instance-Of@Frame-Ontology (Nth ?Tuple ?N) ?Type))))))