Class UNARY-RELATION

Slots on this class:

Documentation:
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).
Instance-Of: Class
Subclass-Of: Relation

Slots on instances of this class:

Arity: 1

Equivalence Axioms:

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

Axioms:

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

(Not (Empty ?Relation))

(Relation ?Relation)

Other Related Axioms:

(<= (Arity $X 1) (Unary-Relation $X))

(=> (Unary-Relation ?Relation) (= (Arity ?Relation) 1))

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

Notes: