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The Basics |
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Arity |
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Argument Types |
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Second-Order Predicates |
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More on Functions |
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Know what type of thing a given function returns
for any appropriate argument |
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#$MotherFn always returns some female animal |
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#$TransportViaFn always returns some collection of transportation events |
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In CycL it’s easy to specify function result
types ... |
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Specified in two primary ways |
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#$resultIsa :
states what type of thing the result is an instance of |
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#$resultGenl :
states what type of thing the result is a specialization of |
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Example 1 |
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(#$resultIsa #$GovernmentFn #$RegionalGovernment) |
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Thus
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(#$isa
(#$GovernmentFn
#$Sweden)
#$RegionalGovernment) and |
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(#$isa
(#$GovernmentFn #$CityofAustinTX)
#$RegionalGovernment) |
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Example 2 |
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(#$resultIsa
#$TransportViaFn
#$Collection) and |
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(#$resultGenl
#$TransportViaFn #$TransportationEvent) |
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Thus , |
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(#$TransportViaFn
#$Automobile) is an instance of #$Collection |
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and a specialization of #$TransportationEvent |
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Given the
transitivity of #$genls and
the “transfer of #$isa through #$genls” result types are powerful. |
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Example (using transitivity of #$genls) : |
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(#$resultGenl
#$TransportViaFn #$TransportionEvent)
and |
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(#$genls
#$TransportationEvent
#$Event) |
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Thus , |
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(#$genls
(#$TransportViaFn
#$Automobile) #$Event) |
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Example (using
“transfer of #$isa through #$genls”) : |
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(#$resultIsa
#$GovernmentFn #$RegionalGovernment) and |
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(#$genls
#$RegionalGovernment
#$Organization) |
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Thus
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(#$isa (#$GovernmentFn #$Sweden) #$Organization) |
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Given this information : |
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(#$isa #$BodyPartFn
#$BinaryFunction) |
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(#$arg1Isa
#$BodyPartFn #$Animal) |
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(#$arg2Isa
#$BodyPartFn
#$AnimalBodyPartType) |
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(#$arg2Isa
#$BodyPartFn
#$UniqueAnatomicalBodyPartType) |
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(#$arg2Genl
#$BodyPartFn
#$AnimalBodyPart) |
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(#$resultIsa
#$BodyPartFn
#$AnimalBodyPart) |
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Are these well-formed NATs ? |
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(#$BodyPartFn
#$SubaruCar #$Fender) |
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(#$BodyPartFn
#$GoldenRetriever #$Tail) |
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(#$BodyPartFn
#$Rover) |
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(#$BodyPartFn
#$Rover #$Tail) |
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Given this information : |
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(#$isa #$BodyPartFn
#$BinaryFunction) |
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(#$arg1Isa
#$BodyPartFn #$Animal) |
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(#$arg2Isa
#$BodyPartFn
#$AnimalBodyPartType) |
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(#$arg2Isa
#$BodyPartFn
#$UniqueAnatomicalBodyPartType) |
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(#$arg2Genl
#$BodyPartFn
#$AnimalBodyPart) |
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(#$resultIsa
#$BodyPartFn
#$AnimalBodyPart) |
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Are these well-formed NATs ? |
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(#$BodyPartFn
#$SubaruCar #$Fender) |
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(#$BodyPartFn
#$GoldenRetriever #$Tail) |
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(#$BodyPartFn
#$Rover) |
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(#$BodyPartFn
#$Rover #$Tail) |
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Given this information : |
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(#$isa #$BodyPartFn
#$BinaryFunction) |
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(#$arg1Isa
#$BodyPartFn #$Animal) |
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(#$arg2Isa
#$BodyPartFn
#$AnimalBodyPartType) |
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(#$arg2Isa
#$BodyPartFn
#$UniqueAnatomicalBodyPartType) |
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(#$arg2Genl
#$BodyPartFn
#$AnimalBodyPart) |
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(#$resultIsa
#$BodyPartFn
#$AnimalBodyPart) |
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Are these well-formed NATs ? |
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(#$BodyPartFn
#$SubaruCar #$Fender) |
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(#$BodyPartFn
#$GoldenRetriever #$Tail) |
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(#$BodyPartFn
#$Rover) |
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(#$BodyPartFn
#$Rover #$Tail) |
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Given this information : |
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(#$isa #$InstructionsFn-Making #$UnaryFunction) |
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(#$arg1Isa
#$InstructionsFn-Making
#$ExistingObjectType) |
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(#$arg1Genl
#$InstructionsFn-Making
#$Artifact-Generic) |
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(#$resultIsa
#$InstructionsFn-Making
#$ObjectType) |
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(#$resultGenl
#$InstructionsFn-Making
#$Instructions) |
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Are these well-formed NATs ? |
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(#$InstructionsFn-Making #$Recipe #$ChickenSoup) |
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(#$InstructionsFn-Making #$RadioReceiver) |
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(#$InstructionsFn-Making #$Mud) |
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(#$InstructionsFn-Making #$SetOrCollection) |
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Given this information : |
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(#$isa #$InstructionsFn-Making #$UnaryFunction) |
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(#$arg1Isa
#$InstructionsFn-Making
#$ExistingObjectType) |
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(#$arg1Genl
#$InstructionsFn-Making
#$Artifact-Generic) |
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(#$resultIsa
#$InstructionsFn-Making
#$ObjectType) |
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(#$resultGenl
#$InstructionsFn-Making
#$Instructions) |
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Are these well-formed NATs ? |
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(#$InstructionsFn-Making #$Recipe #$ChickenSoup) |
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(#$InstructionsFn-Making #$RadioReceiver) |
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(#$InstructionsFn-Making #$Mud) |
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(#$InstructionsFn-Making #$SetOrCollection) |
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Given this information : |
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(#$isa #$InstructionsFn-Making #$UnaryFunction) |
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(#$arg1Isa
#$InstructionsFn-Making
#$ExistingObjectType) |
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(#$arg1Genl
#$InstructionsFn-Making
#$Artifact-Generic) |
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(#$resultIsa
#$InstructionsFn-Making
#$ObjectType) |
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(#$resultGenl
#$InstructionsFn-Making
#$Instructions) |
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Are these well-formed NATs ? |
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(#$InstructionsFn-Making #$Recipe #$ChickenSoup) |
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(#$InstructionsFn-Making #$RadioReceiver) |
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(#$InstructionsFn-Making #$Mud) |
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(#$InstructionsFn-Making #$SetOrCollection) |
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A key distinction among functions : |
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Does it always return an individual ? |
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#$MotherFn |
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#$BorderBetweenFn |
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Does it always return a collection ? |
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#$TransportViaFn |
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#$GroupFn |
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#$IndividualDenotingFunction |
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All functions such that :
(#$resultIsa ?FUNCTION #$Individual) |
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Any NAT made by applying ?FUNCTION denotes an individual |
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(as
opposed to a collection). |
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Must have a
#$resultIsa specification. |
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Must not have a
#$resultGenl specification. Why
not? |
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More Examples :
#$GovernmentFn , #$BirthFn |
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#$CollectionDenotingFunction |
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All functions such that :
(#$resultIsa ?FUNCTION #$Collection) |
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Any NAT made by applying ?FUNCTION denotes a
collection |
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(as
opposed to an individual). |
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Must have a #$resultIsa specification. |
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May also have a
#$resultGenl specification. |
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Individual vs. Collection Denoting Functions |
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#$Function-Denotational |
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#$Individual #$Collection |
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Denoting disjoint Denoting |
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Function Function |
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#$GovernmentFn
#$BirthFn #$GroupFn #$ResidentsFn |
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isa |
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genls |
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Function result types |
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Transitivity of #$genls |
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Individual-denoting vs. collection-denoting
functions |
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Notes