Class Positive-Integer

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

Subclass-Of@Frame-Ontology:

Integer, Number, Rational-Number, Real-Number

Instance-Of@Frame-Ontology: Class@Frame-Ontology, Relation, Set

Arity@Frame-Ontology: 1

Documentation@Ol%Frame-Ontology:

An integer greater than zero, not including zero. A less ambiguous name for KIF's NATURAL.

---

Slots:

Implication Axioms for Positive-Integer:

(=> (Positive-Integer ?X) (> ?X 0))

Equivalence Axioms for Positive-Integer:

(<=> (Positive-Integer ?X) (And (Integer ?X) (> ?X 0)))

Implication Axioms mentioning Positive-Integer:

(=> (= (Projection@Frame-Ontology ?Relation ?Column)
       ?Projection-Relation)
    (Positive-Integer ?Column))

Equivalence Axioms mentioning Positive-Integer:

(<=> (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))))))

Axioms mentioning Positive-Integer:

(Nth-Domain@Frame-Ontology Projection@Frame-Ontology
            2
            Positive-Integer)

(Nth-Domain@Frame-Ontology Nth-Domain@Frame-Ontology
            2
            Positive-Integer)