Relation Subset

Instance-Of@Frame-Ontology: Binary-Relation@Ol-User%Kif-Relations, Relation@Ol-User%Kif-Relations, Set
Domain@Frame-Ontology: Set
Range@Frame-Ontology: Set
Has-Subrelation@Frame-Ontology: Proper-Subset
Arity@Frame-Ontology: 2
The sentence {tt (subset $tau_1$ $tau_2$)} is true if and only if $tau_1$ and $tau_2$ are sets and the objects in the set denoted by $tau_1$ are contained in the set denoted by $tau_2$.


Implication Axioms for Subset:

(=> (Subset ?S1 ?S2)
    (Forall (?X) (=> (Member ?X ?S1) (Member ?X ?S2))))

Equivalence Axioms for Subset:

(<=> (Subset ?S1 ?S2)
     (And (Set ?S1)
          (Set ?S2)
          (Forall (?X) (=> (Member ?X ?S1) (Member ?X ?S2)))))

Axioms for Subset:

(Set ?S2)

(Set ?S1)

Implication Axioms mentioning Subset:

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

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

(=> (Bounded ?V) (Bounded (Setofall ?U (Subset ?U ?V))))

Equivalence Axioms mentioning Subset:

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

(<=> (Set-Cover ?S @Sets) (Subset ?S (Union @Sets)))

Axioms mentioning Subset:

(<= (Subset Ontolingua-Internal::@Arg-List)
    (Proper-Subset Ontolingua-Internal::@Arg-List))