![]() | Sets and Individuals in CYC® |
![]() | CYC® Predicates |
CYC® constants can either denote sets, like "the set of all people", or individuals, like "the Eiffel Tower". Every term in CYC® is an element of #$Thing, the universal set. #$Thing is partitioned into #$Individual and #$SetOrCollection.
#$Individual denotes the set of all things which are not sets. Individuals in the CYC® KB include constants such as #$CityOfSanFrancisco and #$JimmyCarter.
#$SetOrCollection is partitioned into #$Set-Mathematical and #$Collection. The distinction between mathematical sets and collections in CYC® is an important one. Both sets and collections can have elements. Thus, they can both enter into set-theoretic relations like "subset" and "superset".
The difference between #$Collection and #$Set-Mathematical is that sets, in the mathematical sense, are defined extensionally -- that is, by their members. Two sets that have the same members are equivalent. CYC® collections, on the other hand, are defined intensionally, by their criteria for membership. So in CYC®, #$USPresidentsNamedRoosevelt, #$USPresidentsWhoWereEachOthersFifthCousins, and #$TheFirstTwoUSPresidentsWhoseLastNamesBeginWithR would all be different #$Collections, even though they are all comprised of exactly the same elements as the mathematical set {Theodore Roosevelt, Franklin Delano Roosevelt}.
In CYC®, collections are much more important, and much more commonly used, than sets. The criteria for membership in a #$Collection need not be stated explicitly in the KB. Collections in the CYC® KB include #$Dog (the collection of all dogs), #$RealNumber (the collection of all real numbers), and #$Buying (the collection of all buying events).
Membership in a collection is typically expressed as "instance of" or "element of" or "is a", as in "Fred is an instance of the collection #$Person," or "Fred is an element of #$Person," or "Fred is a #$Person." If the terms "subset" and "superset" are used with reference to collections, they typically are intended to mean "more specific collection" and "more general collection", respectively.