Predicates and Denotational Functions The Basics Arity Argument
Predicates and Denotational Functions • • • The Basics Arity Argument Types Second-Order Predicates More on Functions Copyright © 2002 Cycorp
Argument Types The types of arguments a predicate or function requires. • While this is a term : (#$Mother. Fn #$Hillary. Clinton) • There’s something odd about : (#$Mother. Fn #The. White. House) The White House is not the kind of thing that can have a mother. • #$The. White. House (unlike #$Hillary. Clinton) is not an appropriate type of argument for #$Mother. Fn • We can state in Cyc. L the type(s) of arguments appropriate for a given predicate or function. . Copyright © 2002 Cycorp
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 Copyright © 2002 Cycorp
Argument Types Example 1 • • (#$arg 1 Isa #$mother #$Animal) (#$arg 2 Isa #$mother #$Female. Animal) Thus , (#$mother #$Chelsea. Clinton #$Hillary. Clinton) is a well-formed sentence because : (#$isa #$Chelsea. Clinton #$Animal) and (#$isa #$Hillary. Clinton #$Female. Animal) Copyright © 2002 Cycorp
Argument Types Example 2 • (#$arg 1 Isa #$Transport. Via. Fn #$Existing. Object. Type) • (#$arg 1 Genl #$Transport. Via. Fn #$Solid. Tangible. Thing) Thus , (#$Transport. Via. Fn #$Automobile) is #$Automobile is both: a well-formed NAT because an instance of #$Existing. Object. Type and a specialization of #$Solid. Tangible. Thing. Copyright © 2002 Cycorp
Argument Types A relation must be applied to arguments that meet its argument type specifications for the result to be semantically wellformed. • (#$Mother. Fn #$The. White. House) is semantically malformed. • (#$Mother. Fn #$Hillary. Clinton) is semantically well-formed. Cf. A relation must be applied to the proper number of arguments for its arity for the result to be syntactically well-formed. Copyright © 2002 Cycorp
Examples of Predicate Use Given this information : (#$isa #$object. Has. Color #$Binary. Predicate) (#$arg 1 Isa #$object. Has. Color #$Spatial. Thing-Localized) (#$arg 2 Isa #$object. Has. Color #$Color) Are these well-formed formulas ? (#$object. Has. Color #$Golden. Retriever #$Tan. Color $Gold. Color) #$Emerald-Gem #$Green. Color) #$The. White. House #$White. Color) #$The. White. House #$Pink. Color) Copyright © 2002 Cycorp
Examples of Predicate Use Given this information : (#$isa #$object. Has. Color #$Binary. Predicate) (#$arg 1 Isa #$object. Has. Color #$Spatial. Thing-Localized) (#$arg 2 Isa #$object. Has. Color #$Color) Are these well-formed formulas ? (#$object. Has. Color #$Golden. Retriever #$Tan. Color $Gold. Color) #$Emerald-Gem #$Green. Color) #$The. White. House #$White. Color) #$The. White. House #$Pink. Color) Copyright © 2002 Cycorp
Examples of Predicate Use Given this information : (#$isa #$object. Has. Color #$Binary. Predicate) (#$arg 1 Isa #$object. Has. Color #$Spatial. Thing-Localized) (#$arg 2 Isa #$object. Has. Color #$Color) Are these well-formed formulas ? (#$object. Has. Color #$Golden. Retriever #$Tan. Color $Gold. Color) #$Emerald-Gem #$Green. Color) #$The. White. House #$White. Color) #$The. White. House #$Pink. Color) Copyright © 2002 Cycorp
Summary • Each predicate and function is defined to use arguments of particular types • Argument types can be specified in two ways • #$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 Copyright © 2002 Cycorp
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