Notes

Outline

Predicates and Denotational Functions


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

Argument Types


	The types of arguments a predicate or function requires.

Argument Types


	Argument types can be specified two ways

	#$arg[N]Isa : states what the Nth argument must be an instance of

	#$arg[N]Genl : states what the Nth argument must be a specialization of

Argument Types


	Example 1

	(#$arg1Isa #$mother #$Animal)
	(#$arg2Isa #$mother #$FemaleAnimal)

	Thus ,

		(#$mother #$ChelseaClinton #$HillaryClinton)

		is a well-formed sentence because :
			(#$isa #$ChelseaClinton #$Animal) and
			(#$isa #$HillaryClinton #$FemaleAnimal)

Argument Types


	Example 2

	(#$arg1Isa #$TransportViaFn #$ExistingObjectType)
	(#$arg1Genl #$TransportViaFn #$SolidTangibleThing)

		Thus ,
	(#$TransportViaFn #$Automobile) is a well-formed NAT because #$Automobile is both:
			an instance of #$ExistingObjectType
		and
			a specialization of #$SolidTangibleThing.

Argument Types


	A relation must be applied to arguments that meet its argument type specifications for the result to be semantically well-formed.

	(#$MotherFn #$TheWhiteHouse) is semantically malformed.
	(#$MotherFn #$HillaryClinton) is semantically well-formed.

Examples of Predicate Use

Examples of Predicate Use

Examples of Predicate Use

Summary


	Each predicate and function is defined to use arguments of particular types
	Argument types can be specified in two ways
			#$arg[N]Isa
			#$arg[N]Genl
	A relation must be applied to arguments that meet its argument type specifications if the result is to be semantically well-formed