Class Simple-Set

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

Subclass-Of@Frame-Ontology:

Bounded, Bounded, Set, Set, Thing@Frame-Ontology ...

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

Arity@Frame-Ontology: 1

Documentation@Ol%Frame-Ontology:

A simple set is a set that can be a member of another set.

Notes:

• The constraint that simple-set is a subclass-of thing is specified as part of the definition of THING, but it needs to be here, too, for bootstrapping reasons.
• Source: KIF Version 3.0 Specification

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Slots:

Equivalence Axioms for Simple-Set:

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

Frame References to Simple-Set:

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

Exhaustive-Subclass-Partition@Frame-Ontology: {Individual-Thing@Frame-Ontology, Simple-Set}

Implication Axioms mentioning Simple-Set:

(=> (= (Generalized-Union ?Set-Of-Sets) ?Set)
    (Forall (?S) (=> (Member ?S ?Set-Of-Sets) (Simple-Set ?S))))

(=> (= (Generalized-Intersection ?Set-Of-Sets) ?Set)
    (Forall (?S) (=> (Member ?S ?Set-Of-Sets) (Simple-Set ?S))))