Notes

Outline

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

Predicates and Denotational Functions

#$Predicate  Some instances of #$Predicate #$mother #$objectHasColor #$memberStatusOfOrganization  Predicates are used to make  sentences

#$Predicate  Some instances of  #$Predicate #$mother #$objectHasColor #$memberStatusOfOrganization

#$Predicate A sentence built from a predicate is either True or False. (#$mother  #$ChelseaClinton  #$HillaryClinton)   is True (#$physicalParts  #$TheWhiteHouse  #$TheLincolnMemorial) is False  Predicates are thus truth-functional relations.

#$Predicate    Truth or falsity of such sentences depends on facts about the world rather than logic alone. (#$mother  #$ChelseaClinton  #$HillaryClinton)      is True because Hillary is Chelsea’s mother. (#$physicalParts  #$TheWhiteHouse  #$TheLincolnMemorial)    is False because the Lincoln Memorial is not part of the White House.    Predicates are thus extra-logical relations.

#$Function-Denotational Instances of  #$Function-Denotational #$MotherFn #$BorderBetweenFn #$GroupFn

#$Function-Denotational Instances of  #$Function-Denotational #$MotherFn #$BorderBetweenFn #$GroupFn

#$Function-Denotational Terms built from functions denote things: (#$MotherFn  #$ChelseaClinton)  denotes HillaryClinton (#$BorderBetweenFn  #$Sweden  #$Norway)  denotes the border between Sweden and Norway. Use the last example as a term (or “name”) for the border between Sweden and Norway Apply a predicate or function to it if we want to

How to Tell The Difference Between Predicates and Functions in CycL Names of predicates always begin with a lower-case letter. Names of functions often include the string ‘Fn’. Example:   #$mother  vs.  #$MotherFn (#$mother  $ChelseaClinton  #$HillaryClinton) (#$MotherFn  #$ChelseaClinton) Example:  #$sponsors  vs.  #$SponsorFn-Agent (#$sponsors  #$GeneralMotors  #$USOlympicTeam) (#$SponsorFn-Agent  #$USOlympicTeam)

Two Central Features of Predicates and Functions Every predicate and function has Arity:  How many arguments does it require? Argument types:  What types of arguments                  does it require?

Summary Predicates are used to make sentences Predicates are truth-functional relations Predicates are extra-logical relations Functions are used to make non-atomic terms (NATs) NATs denote things Differentiating between predicates and functions in CycL Two central features of predicates and functions are arity and argument types