Class Unary-Relation

Subclass-Of@Frame-Ontology: Relation, Set
Instance-Of@Frame-Ontology: Class@Frame-Ontology, Relation, Set
Arity@Frame-Ontology: 1
Inherited-Slot-Value@Frame-Ontology: 1
A unary relation is a relation of arity 1. Unary relations are the same thing as classes. In this ontology there is no logical distinction between a monadic predicate (unary relation) and a type (class).


  • See-Also: class
  • originally defined in the KIF-RELATIONS ontology


Arity@Frame-Ontology: 1

Implication Axioms for Unary-Relation:

(=> (Unary-Relation ?Relation)
    (Forall (?Tuple) (=> (Member ?Tuple ?Relation) (Single ?Tuple))))

(=> (Unary-Relation ?Relation) (Not (Empty ?Relation)))

(=> (Unary-Relation ?Relation)
    (= (Arity@Frame-Ontology ?Relation) 1))

Equivalence Axioms for Unary-Relation:

(<=> (Unary-Relation ?Relation)
     (And (Relation ?Relation)
          (Not (Empty ?Relation))
          (Forall (?Tuple)
                  (=> (Member ?Tuple ?Relation) (Single ?Tuple)))))