The sentence {tt (member $tau_1$ $tau_2$)} is true if and only if the object denoted by $tau_1$ is contained in the set denoted by $tau_2$. As mentioned above, an object can be a member of another object if and only if the former is bounded and the latter is a set.Notes:
- Source: KIF Version 3.0 Specification
(=> (= (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)))) (=> (And (Set ?S1) (Set ?S2)) (<=> (Forall (?X) (<=> (Member ?X ?S1) (Member ?X ?S2))) (= ?S1 ?S2))) (=> (Subset ?S1 ?S2) (Forall (?X) (=> (Member ?X ?S1) (Member ?X ?S2)))) (=> (And (Bounded ?U) (Forall (?X) (=> (Member ?X ?U) (Bounded ?X)))) (Bounded (Generalized-Union ?U)))
(<=> (Subset ?S1 ?S2) (And (Set ?S1) (Set ?S2) (Forall (?X) (=> (Member ?X ?S1) (Member ?X ?S2))))) (<=> (Instance-Of@Frame-Ontology ?Individual ?Class) (Member (Listof ?Individual) ?Class)) (<=> (All-Instances@Frame-Ontology ?Class) (And (Class@Frame-Ontology ?Class) (Set ?Set-Of-Instances) (Forall (?Instance) (<=> (Member ?Instance ?Set-Of-Instances) (Instance-Of@Frame-Ontology ?Instance ?Class))))) (<=> (One-Of@Frame-Ontology @Members) (Forall (?Instance) (<=> (Instance-Of@Frame-Ontology ?Instance ?Class) (Member ?Instance (Setof @Members))))) (<=> (Subrelation-Of@Frame-Ontology ?Child-Relation ?Parent-Relation) (And (Relation@Ol-User%Kif-Relations ?Child-Relation) (Relation@Ol-User%Kif-Relations ?Parent-Relation) (Forall (?Tuple) (=> (Member ?Tuple ?Child-Relation) (Member ?Tuple ?Parent-Relation)))))
(Forall (?S) (=> (Not (Empty ?S)) (Exists (?U) (And (Member ?U ?S) (Disjoint ?U ?S))))) (Exists (?S) (And (Set ?S) (Forall (?X) (=> (Member ?X ?S) (Double@Ol-User%Kif-Lists ?X))) (Forall (?X ?Y ?Z) (=> (And (Member (Listof ?X ?Y) ?S) (Member (Listof ?X ?Z) ?S)) (= ?Y ?Z))) (Forall (?U) (=> (And (Bounded ?U) (Not (Empty ?U))) (Exists (?V) (And (Member ?V ?U) (Member (Listof ?U ?V) ?S))))))) (Exists (?U) (And (Bounded ?U) (Not (Empty ?U)) (Forall (?X) (=> (Member ?X ?U) (Exists (?Y) (And (Member ?Y ?U) (Proper-Subset ?X ?Y))))))) (Forall (?Class) (=> (Member ?Class ?Set-Of-Classes) (Class@Frame-Ontology ?Class)))