Function Inverse

• Defined in ontology: Kif-relations
• Source pathname: /tmp_mnt/vol/q/htw/cms/ontolingua/examples/kif/../../all-ontologies/kif/kif-relations.lisp

Instance-Of@Frame-Ontology:

Binary-Relation, Function, Relation, Set

Domain@Frame-Ontology: Binary-Relation

Range@Frame-Ontology: Binary-Relation

Inverse: Inverse

Arity@Frame-Ontology: 2

Documentation@Ol%Frame-Ontology:

One binary relation is the inverse of another if they are equivalent when their arguments are swapped.

Notes:

• Note that INVERSE is a function. It is possible to have more than one relation constant naming the inverse of a relation, but they are all = to each other.
• originally defined in the KIF-RELATIONS ontology

Implication Axioms for Inverse:

(=> (Inverse ?Binary-Relation)
    (<=> (Holds ?Binary-Relation ?X ?Y)
         (Holds (Inverse ?Binary-Relation) ?Y ?X)))

Frame References to Inverse:

In class@frame-ontology One-To-Many-Relation@Frame-Ontology:

Slots:

Inverse:

Slot-Cardinality@Frame-Ontology: 1

Slot-Value-Type@Frame-Ontology: Function

In relation >:

Inverse: <

In relation Has-Subrelation@Frame-Ontology:

Inverse: Subrelation-Of@Frame-Ontology

In relation Superclass-Of@Frame-Ontology:

Inverse: Subclass-Of@Frame-Ontology

In relation Domain-Of@Frame-Ontology:

Inverse: Domain@Frame-Ontology

In class@frame-ontology One-To-One-Relation@Frame-Ontology:

Slots:

Inverse:

Implication Axioms mentioning Inverse:

(=> (Many-Many ?R) (Not (Function (Inverse ?R))))

(=> (Many-To-Many-Relation@Frame-Ontology ?R)
    (Not (Function (Inverse ?R))))

Equivalence Axioms mentioning Inverse:

(<=> (One-One ?R)
     (And (Binary-Relation ?R)
          (Function ?R)
          (Value-Type@Frame-Ontology ?R Inverse Function)
          (Value-Cardinality@Frame-Ontology ?R Inverse 1)))

(<=> (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)))))

(<=> (One-To-One-Relation@Frame-Ontology ?R)
     (And (Unary-Function ?R)
          (Value-Type@Frame-Ontology ?R Inverse Function)
          (Value-Cardinality@Frame-Ontology ?R Inverse 1)))

(<=> (One-To-Many-Relation@Frame-Ontology ?R)
     (And (Binary-Relation ?R)
          (Value-Type@Frame-Ontology ?R Inverse Function)
          (Value-Cardinality@Frame-Ontology ?R Inverse 1)))