A binary relation maps instances of a class to instances of another class. Its arity is 2. Binary relations are often shown as slots in frame systems.Notes:
- originally defined in the KIF-RELATIONS ontology
(=> (Binary-Relation ?Relation) (Forall (?Tuple) (=> (Member ?Tuple ?Relation) (Double ?Tuple)))) (=> (Binary-Relation ?Relation) (Not (Empty ?Relation))) (=> (Binary-Relation ?Relation) (= (Arity@Frame-Ontology ?Relation) 2))
(<=> (Binary-Relation ?Relation) (And (Relation ?Relation) (Not (Empty ?Relation)) (Forall (?Tuple) (=> (Member ?Tuple ?Relation) (Double ?Tuple)))))
(=> (One-One ?R) (Binary-Relation ?R)) (=> (Many-One ?R) (Binary-Relation ?R)) (=> (One-Many ?R) (Binary-Relation ?R)) (=> (Many-Many ?R) (Binary-Relation ?R)) (=> (Unary-Function ?F) (Binary-Relation ?F))
(<=> (One-One ?R) (And (Binary-Relation ?R) (Function ?R) (Value-Type@Frame-Ontology ?R Inverse Function) (Value-Cardinality@Frame-Ontology ?R Inverse 1))) (<=> (Many-One ?R) (And (Binary-Relation ?R) (Function ?R))) (<=> (One-Many ?R) (And (Binary-Relation ?R) (Value-Type@Frame-Ontology ?R Inverse Function) (Value-Cardinality@Frame-Ontology ?R Inverse 1))) (<=> (Many-Many ?R) (And (Binary-Relation ?R) (Not (Function ?R)) (Not (Function (Inverse ?R))))) (<=> (Unary-Function ?F) (And (Function ?F) (Binary-Relation ?F)))
(Nth-Domain@Frame-Ontology Composition 3 Binary-Relation) (Nth-Domain@Frame-Ontology Composition 2 Binary-Relation) (Nth-Domain@Frame-Ontology Composition 1 Binary-Relation) (Nth-Domain@Frame-Ontology Value-Cardinality@Frame-Ontology 2 Binary-Relation) (Nth-Domain@Frame-Ontology Slot-Cardinality@Frame-Ontology 2 Binary-Relation)