Predicates and Denotational Functions

Predicates and Denotational Functions • The Basics • Arity • Argument Types • Second-Order Predicates • More on Functions

Function Result Types • Know what type of thing a given function returns for any appropriate argument • #$MotherFn always returns some female animal • #$TransportViaFnalways returns some collection of transportation events • In CycL it’s easy to specify function result types ...

Function Result Types • Specified in two primary ways • #$resultIsa : states what type of thingthe result is an instance of • #$resultGenl: states what type of thing the result is a specialization of

Function Result Types: #$resultIsa Example 1 (#$resultIsa #$GovernmentFn #$RegionalGovernment) Thus , (#$isa (#$GovernmentFn #$Sweden) #$RegionalGovernment) and (#$isa (#$GovernmentFn #$CityofAustinTX) #$RegionalGovernment)

Function Result Types: #$resultIsa and #$resultGenl Example 2 • (#$resultIsa #$TransportViaFn #$Collection) and • (#$resultGenl #$TransportViaFn #$TransportationEvent) • Thus , (#$TransportViaFn #$Automobile) is an instance of #$Collection and a specialization of #$TransportationEvent

Transitivity of #$genls • Given the transitivity of#$genls and the “transfer of#$isathrough #$genls” result types are powerful. • Example (using transitivity of #$genls) : • (#$resultGenl #$TransportViaFn #$TransportionEvent) and • (#$genls #$TransportationEvent #$Event) Thus , • (#$genls (#$TransportViaFn #$Automobile) #$Event)

Transitivity of #$genls Example • Example (using “transfer of #$isa through #$genls”) : • (#$resultIsa #$GovernmentFn #$RegionalGovernment)and • (#$genls #$RegionalGovernment #$Organization) • Thus , (#$isa (#$GovernmentFn #$Sweden) #$Organization)

Examples of Function Use: #$BodyPartFn Given this information : (#$isa #$BodyPartFn #$BinaryFunction) (#$arg1Isa #$BodyPartFn #$Animal) (#$arg2Isa #$BodyPartFn #$AnimalBodyPartType) (#$arg2Isa #$BodyPartFn #$UniqueAnatomicalBodyPartType) (#$arg2Genl #$BodyPartFn #$AnimalBodyPart) (#$resultIsa #$BodyPartFn #$AnimalBodyPart) Are these well-formed NATs ? (#$BodyPartFn #$SubaruCar #$Fender) (#$BodyPartFn #$GoldenRetriever #$Tail) (#$BodyPartFn #$Rover) (#$BodyPartFn #$Rover #$Tail)

Examples of Function Use: #$InstructionsFn-Making Given this information : (#$isa #$InstructionsFn-Making #$UnaryFunction) (#$arg1Isa #$InstructionsFn-Making #$ExistingObjectType) (#$arg1Genl #$InstructionsFn-Making #$Artifact-Generic) (#$resultIsa #$InstructionsFn-Making #$ObjectType) (#$resultGenl #$InstructionsFn-Making #$Instructions) Are these well-formed NATs ? (#$InstructionsFn-Making #$Recipe #$ChickenSoup) (#$InstructionsFn-Making #$RadioReceiver) (#$InstructionsFn-Making #$Mud) (#$InstructionsFn-Making #$SetOrCollection)

Individuals or Collections? A key distinction among functions : • Does it always return an individual ? • #$MotherFn • #$BorderBetweenFn • Does it always return a collection ? • #$TransportViaFn • #$GroupFn

#$IndividualDenotingFunction #$IndividualDenotingFunction • All functions such that : (#$resultIsa ?FUNCTION #$Individual) • Any NAT made by applying ?FUNCTION denotes an individual (as opposed to a collection). • Must have a #$resultIsa specification. • Must not have a #$resultGenl specification. Why not? • More Examples : #$GovernmentFn , #$BirthFn

#$CollectionDenotingFunction #$CollectionDenotingFunction • All functions such that :(#$resultIsa ?FUNCTION #$Collection) • Any NAT made by applying ?FUNCTION denotes a collection (as opposed to an individual). • Must have a #$resultIsa specification. • May also have a#$resultGenlspecification. • More Examples : #$ResidentsFn , #$TeacherFn)

The Hierarchy Individual vs. Collection Denoting Functions #$Function-Denotational #$Individual Denoting Function #$Collection Denoting Function disjoint #$GovernmentFn #$BirthFn #$GroupFn #$ResidentsFn isa genls

Summary • Function result types • Transitivity of #$genls • Individual-denoting vs. collection-denoting functions

Predicates and Denotational Functions