9.9.1 Quantifier

Overview

As will be recalled, there are two types of quantifiers:

  1. The existential quantifier, or
  2. A defined quantifier.

The existential quantifier

The existential quantifier is represented either by a blank (i.e., by nothing) or by the symbol . It may be paraphrased as "There is a" or simply "a". For example:

   [Cat]->(On)->[Mat]
   "A cat is on a mat"

Since the referent is blank for both of these concepts, the quantifier is also blank. Since a blank quantifier is the existential quantifier, this means that we can paraphrase this graph as "There is a cat, and there is a mat, and the cat is on the mat".

Defined quantifiers

A "defined quantifier" is defined as "a quantifier which can be defined in terms of the existential quantifier." This definition does not help much in understanding what it is, of course, so instead we give some examples:

Universal quantifier

The quantifier means "for all". It is also called the "universal quantifier", since it means that the referent refers to all instances of the given type. For example:

   [LivingFish: ]->(Attr)->[Wet]
   "All living fish have an attribute which is wet"
   "All living fish are wet"

Unspecified set-quantifier

The "{*}" quantifier means "a set of things". It can be used to indicate plural. For example:

   [Bird: {*}]

means "There are some birds" or simply "Birds".

With this definition, we can finally represent the real line from "Dream a little dream of me":

   [Sing]->(Agnt)->[Bird: {*}]->(In)->[SycamoreTree]
   "Some birds are the agent of sing.  The birds are in a sycamore
      tree" 
   "Birds singing in a sycamore tree"

Quantities with {*}

This notation can also be extended with the count of elements in the set:

   [Guest: {*}@40]<-(Agnt)<-[Give]-
                       ->(Rcpt)->[Person: Alfred],
                       ->(Thme)->[Present: {*}@37]
   "Forty guests give Alfred 37 presents"

Quantities on their own

Quantities may also be on their own, without the {*} set notation, and they may have units, such as seconds or kgs:

   [Person]->(Has)->[Leg: @2]
   "There exists a person who has two legs"

   [Song: HappyBirthdayToYou]->(Dur)->[Interval: @18 sec]
   "Happy Birthday To You has a duration which is an interval which
      has length 18 seconds"
   "Happy Birthday To You lasts 18 seconds"

Collections

Collections, such as {1,2,5} or {Tom,Julia,Brad}, may also be used as quantifiers:

   [Guest: {Tom,Julia,Brad}]<-(Agnt)<-[Sing]-
               ->(Thme)->[Song: HappyBirthdayToYou]
               ->(To)->[Person: Alfred]
   "The guests, Tom, Julia, and Brad, sing a song, 
      'Happy Birthday to you,' 
      to Alfred".


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