Relation Proper-Subset

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

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

Subrelation-Of@Frame-Ontology: Subset

Arity@Frame-Ontology: 2

Documentation@Ol%Frame-Ontology:

The sentence {tt (proper-subset $tau_1$ $tau_2$)} is true if the set denoted by $tau_1$ is a subset of the set denoted by $tau_2$ but not vice-versa.

Notes:

• Source: KIF Version 3.0 Specification

Implication Axioms for Proper-Subset:

(=> (Proper-Subset ?S1 ?S2) (Not (Subset ?S2 ?S1)))

(=> (Proper-Subset ?S1 ?S2) (Subset ?S1 ?S2))

Equivalence Axioms for Proper-Subset:

(<=> (Proper-Subset ?S1 ?S2)
     (And (Subset ?S1 ?S2) (Not (Subset ?S2 ?S1))))

Axioms mentioning Proper-Subset:

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