A set is a collection of objects, both individuals and sets of various sorts. It is a KIF primitive.Notes:
- Source: KIF Version 3.0 Specification
(=> (Union @Sets ?Set) (Set ?Set)) (=> (Intersection @Sets ?Set) (Set ?Set)) (=> (= (Union @Sets) ?Set) (=> (Item@Ol-User%Kif-Lists ?S (Listof @Sets)) (Set ?S))) (=> (= (Intersection @Sets) ?Set) (=> (Item@Ol-User%Kif-Lists ?S (Listof @Sets)) (Set ?S))) (=> (= (Difference ?Set @Sets) ?Diff-Set) (=> (Item@Ol-User%Kif-Lists ?S (Listof @Sets)) (Set ?S)))
(<=> (Individual ?X) (Not (Set ?X))) (<=> (Simple-Set ?X) (And (Set ?X) (Bounded ?X))) (<=> (Subset ?S1 ?S2) (And (Set ?S1) (Set ?S2) (Forall (?X) (=> (Member ?X ?S1) (Member ?X ?S2))))) (<=> (Cardinality@Ol-User%Kif-Extensions ?Set) (And (Set ?Set) (Exists (@Elements) (And (= ?Set (Setof @Elements)) (= ?Integer (Length@Ol-User%Kif-Lists (Listof @Elements))))))) (<=> (Finite-Set@Ol-User%Kif-Extensions ?F-Set) (And (Set ?F-Set) (Exists (@Elements) (= ?F-Set (Setof @Elements)))))
(Nth-Domain@Frame-Ontology Difference 3 Set) (Nth-Domain@Frame-Ontology Difference 1 Set) (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))))))) (Nth-Domain@Frame-Ontology Has-Values@Ol-User%Slot-Constraint-Sugar 3 Set)