Axiom Axiom-Of-Infinity

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

Documentation@Ol%Frame-Ontology:

There is a bounded set containing a set, a set that properly contains that set, a third set that properly contains the second set, and so forth. In short, there is at least one bounded set of infinite cardinality.

Notes:

• Source: KIF Version 3.0 Specification

Defining axiom of Axiom-Of-Infinity:

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