English fol universal quantifier
This presentation is the property of its rightful owner.
Sponsored Links
1 / 6

English  FOL: universal quantifier PowerPoint PPT Presentation


  • 89 Views
  • Uploaded on
  • Presentation posted in: General

English  FOL: universal quantifier. The structure of the universal quantifier is:  X(...  ...) Key words in an English sentence that indicates an universal quantifier: all , every, each, any For every x, if x is a student and x likes mathematics, the x does not likes Oscar:

Download Presentation

English  FOL: universal quantifier

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


English fol universal quantifier

English  FOL: universal quantifier

The structure of the universal quantifier is:

X(... ...)

Key words in an English sentence that indicates an universal quantifier:

all , every, each, any

For every x, if x is a student and x likes mathematics, the x does not likes Oscar:

(1) X(S (X)  M(X)  L(X, o))


English fol universal quantifier1

English  FOL: universal quantifier

  • no (when negating an existential quantifier):

    No student who likes mathematics also likes Oscar.

    There does not exist an x such that x is a student and x likes mathematics and x likes Oscar.

    (2) X(S (X)  M(X)  L(X, o))

    (1) is equivalent to (2) :

    ||= ((1) <=> (2))


English fol existential quantifier

English  FOL: existential quantifier

The structure of the existential quantifier is:

 X(... ...)

Key words in an English sentence that indicates an existential quantifier:

  • some, there is, there are, there exists, at least one

    There is an x such that x is a student pilot, and there is a y so that y is an instructor and x flies to chicago with y, but it is not the case that x attends a meeting and x is accompanied by y:

    (3) X(SP(X) Y (I(Y)  F(X, c, Y) 

     (M(X)  A(X, Y))))


English fol existential quantifier1

English  FOL: existential quantifier

  • not all (when negating an universal quantifier):

    Not all student pilots who fly a plane to Chicago with an instructor attend a meeting accompanied by the instructor.

    (4) X(SP(X)  (Y ((I(Y)  F(X, c, Y)) 

    (M(X)  A(X, Y))))

    (3) is equivalent to (4) :

    ||= ((3) <=> (4))


English fol ambiguities

English  FOL: ambiguities

There are no hard and fast rules for translating English into FOL.

For example, the articles ”a” or “an” in some cases imply an existential quantifier and in others an universal quantifier.

Oscar flies a plane to Chicago with an instructor:

 X(I(X)  F(o, c, X)

A student will do well at college if he/she studies:

X(S(X)  D(X) W(x))


English fol ambiguities1

English  FOL: ambiguities

Another ambiguity that occurs in English is that plural nouns not preceded by “all” or “some” are sometimes translated using a universal quantifier. At other times, these nouns are translated using an existential quantifier.

Viruses cause colds (some viruses cause colds)

Cats are animals (all cats are animals)

The translations depends upon the meaning, and in some cases, the meaning may not be clear. The problem is that English is ambiguous, whereas FOL is not.


  • Login