Class Bounded

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

Superclass-Of@Frame-Ontology: Simple-Set, Agent-Name@Agents, Individual-Thing@Frame-Ontology

Instance-Of@Frame-Ontology: Class@Frame-Ontology, Relation@Ol-User%Kif-Relations, Set

Domain-Of@Frame-Ontology: Member

Arity@Frame-Ontology: 1

Documentation@Ol%Frame-Ontology:

Something is bounded if it can be a member of a set. This is a KIF primitive.

Notes:

• Source: KIF Version 3.0 Specification

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Slots:

Frame References to Bounded:

In class@frame-ontology Thing@Frame-Ontology:

Alias@Frame-Ontology: Bounded

Implication Axioms mentioning Bounded:

(=> (Simple-Set ?X) (Bounded ?X))

(=> (Finite-Set@Ol-User%Kif-Extensions ?S) (Bounded ?S))

(=> (And (Bounded ?U) (Forall (?X) (=> (Member ?X ?U) (Bounded ?X))))
    (Bounded (Generalized-Union ?U)))

(=> (And (Bounded ?U) (Set ?S)) (Bounded (Intersection ?U ?S)))

Equivalence Axioms mentioning Bounded:

(<=> (Unbounded ?X) (Not (Bounded ?X)))

(<=> (Simple-Set ?X) (And (Set ?X) (Bounded ?X)))

Axioms mentioning Bounded:

(Exists (?S)
        (And (Set ?S)
             (Forall (?X)
                     (=> (Member ?X ?S)
                         (Double@Ol-User%Kif-Lists ?X)))
             (Forall (?X ?Y ?Z)
                     (=> (And (Member (Listof ?X ?Y) ?S)
                              (Member (Listof ?X ?Z) ?S))
                         (= ?Y ?Z)))
             (Forall (?U)
                     (=> (And (Bounded ?U) (Not (Empty ?U)))
                         (Exists (?V)
                                 (And (Member ?V ?U)
                                      (Member (Listof ?U ?V) ?S)))))))

(Exists (?U)
        (And (Bounded ?U)
             (Not (Empty ?U))
             (Forall (?X)
                     (=> (Member ?X ?U)
                         (Exists (?Y)
                                 (And (Member ?Y ?U)
                                      (Proper-Subset ?X ?Y)))))))