- 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
- Domain@Frame-Ontology: Set
- Range@Frame-Ontology: Set
- Has-Subrelation@Frame-Ontology: Proper-Subset
- Arity@Frame-Ontology: 2
- Documentation@Ol%Frame-Ontology:
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 $tau_2$.
Notes:
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))