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(Back to the [[NMTS_Meeting_2#Groups|group overview]])
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= Wikipage of Group 5 - Quantifiers =
= Quantifiers (Group 5) =
 
=== Comments by the NMTS team ===
 
* die Exercises Kategorie existiert 2 mal, ausgefüllt ist sie aber nur unter dem Inhaltsverzeichnis Punkt 1.2, nicht unter 2.5
* Link zu Glossary Eintrag Quantifiers, der nicht existiert
* die Bilder aus Exercises fehlen in Our pictures
 


== Overview ==
== Overview ==
Line 18: Line 11:
* [[User:AnKa| AnKa]]
* [[User:AnKa| AnKa]]
* [[User:Katharina| Katharina]]
* [[User:Katharina| Katharina]]
* [[User:Lara| Lara]]
* [[User:Lara| Lara]]: [[Lara's Term Paper]]
 


=== Short description of the topic ===
=== Short description of the topic ===
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Quantifiers are words that precede and modify nouns; they indicate quantity.
Quantifiers are words that precede and modify nouns; they indicate quantity.


There are different types of quantifiers which can be divided in quantifiers for count nouns and non-count nouns.
In logic quantification quantifiers bind variables which means that a quantifier connects parts of a sentence which classify a domain of discourse.


There are different types of quantifiers which can be divided in:
*Universal quantifiers (Logical quantifier)
*Existential quantifiers (Logical quantifier)
*Restricted quantifiers


==== Comment ====
Individual variables are written as "x" and can refer to any individual.


Count-nouns are regarded as individual, countable items:
e.g. tree


'''The Universal Quantifier ∀:'''
*The Universal quantifier formalizes the notion that something is true for everything, or every relevant thing.
*Symbol ∀ denotes ''given any'' or ''for all''.
*The sequence "∀x" is read as "For any value of x", "For all values of x" or "Whatever x may be".


Non-count nouns are not countable, things that we regard as 'undifferentiated mass':
e.g. dancing, the water we spilled on the floor, one big mess


'''The Existential Quantifier ∃:'''
*An existential sentence states the existence of at least one thing of the domain.
*Symbol ∃ stands for noun phrases with ''a/an'', ''some'' or ''there exists'' sentences.
*The sequence "∃x" is read as "There is an x" or "There is at least one thing x".
'''The Restricted Quantifier:'''
*Restricted quantifiers point out a proportion of a set, not the proportion of everything there is.
*Sentences which contain restricted quantifiers are written with square brackets.
*Examples: some – several – many – most – a few – a number – one/two/three – no – no one – someone – all – every
'''Scopal Ambiguity:'''
Scopal ambiguity arises when a sentence contains two or more quantifiers. If this is the case the sentence can be understood in different ways. The difference in meaning can be clarified by expressing the sentence with the corresponding logical formulae. Each of these logical forms represents a particular meaning and thus cannot be ambiguous.
<span style="color:#00CC00">For further explanation and exercises please have a look at our [http://user.uni-frankfurt.de/~sailer/nmts-wise1213/Quantifiers_Presentation_final.notebook Presentation] and our [http://youtu.be/6c8TwAdvr9U Podcast].</span>


Nouns that can be either count or non-count nouns:
e.g. paper, stone, and cake
For instance, I can enter a bakery and say 'I want a cake' (an individual bakery product), or, before we enter, I can tell a friend that 'I want cake' and not refer to a specific cake but simply mean that the idea of eating cake appeals to me — any cake or piece of cake with chocolate frosting...




==== Examples ====
==== Examples ====


Quantifier expressions
*some
*both
*all
*everything
*nothing
*at least five
*most
*all but one
*less than half of the
*three books
*more...than
*John and Mary
*only John




Quantifiers that work with count nouns:
'''The Universal Quantifier:'''
 
Every dog is barking.
 
∀x (DOG (x) → BARK (x))
 
''"For every thing x, if x is a dog then x is barking."''
 
 
'''The Existential Quantifier ∃:'''
 
Some birds were singing.
 
∃x (BIRD (x) & SING (x))
 
''"There is at least one thing x such that x is a bird and x sings."''
 
 
'''The Restricted Quantifier:'''
 
Several cars crashed.
 
[Several x: CAR (x)] CRASH (x)
 
 
 
'''Scopal Ambiguity:'''
 
Some students heard both concerts.
 
[Some x: STUDENT (x)] [Both y: CONCERT (y)] HEAR (x, y)
 
''"There exist some students such that each of them heard both concerts."''
 
OR
 
[Both y: CONCERT (y)] [Some x: STUDENT (x)] HEAR (x, y)
 
"Both concerts were such that each, individually, got heard by some students (but not necessarily the same ones)."
 
== References and Links ==
 
=== References ===
<!-- Indicate at least 3 references that you will use for your topic -->
 
 
* Kearns, Kate (2000): ''Semantics''. Basingstoke: Macmillan.
* Swan, Michael (2005): Practical English Usage. 3rd edition. Oxford: Oxford University Press.
*[http://grammar.ccc.commnet.edu/grammar/determiners/determiners.htm | Definition of Quantifiers, Determiners and Articles]
*Explanation of Scopal Ambiguity: http://www.philosophyetc.net/2004/08/scopal-ambiguity.html
 
=== Links ===
<!-- Indicate links that may be helpful for your topic. -->
 
* [http://oxforddictionaries.com/definition/english/quantifier?q=quantifier| Definition of Quantifier from the Oxford Online Dictionary]
* [http://plato.stanford.edu/entries/generalized-quantifiers/| Definition of Quantifier from the Stanford Encylopedia of Philosophy]
 
'''Definitions in the [[Basic Glossary]]:'''
* [[Glossary:Quantifiers | Quantifiers]]


many / a few / several / a couple of / none of the trees
= Our E-Learning Objects =


== Our Wiki Pages ==
<!-- List all the wiki pages that were created by your group. -->


Quantifiers that work with non-count nouns:
'''Definitions in the [[Basic Glossary]]:'''
* [[Glossary:Anaphora| Anaphora]]
* [[Glossary:Paraphrase| Paraphrase]]
* [[Glossary:_Predicate| Predicate]]
* [[Glossary:Prototype| Prototype]]


not much / a little / a bit of / no dancing
== Our Podcasts ==
<!-- List all the podcasts that were created by your group. -->




Quantifiers that work with both count and non-count nouns:
Podcast on Scopal Ambiguity:


all of the / some/ most of the / enough / a lot of trees / lots of / plenty of / a lack of trees/dancing
<embedvideo service="youtube" dimensions="400">http://youtu.be/6c8TwAdvr9U</embedvideo>


== Our Materials for an Interactive Whiteboard ==
<!-- List all the files that your group created for the interactive whiteboard. -->


== Excercises ==
 
Presentation on Quantifiers: [http://user.uni-frankfurt.de/~sailer/nmts-wise1213/Quantifiers_Presentation_final.notebook Quantifiers.notebook]
 
 
== Our exercises ==


The following excercises provide links to their respective solutions. The answer to the question you just worked on is shown on the very top of the new website that pops up.
The following excercises provide links to their respective solutions. The answer to the question you just worked on is shown on the very top of the new website that pops up.
Line 83: Line 151:
Due to long loading times, it might be useful to open the links via right-click, then choose "Open in new tab". In this way you can easily go back to the excercises without loading the group page again. However, at the bottom of each solution, there is a link that leads you back here.
Due to long loading times, it might be useful to open the links via right-click, then choose "Open in new tab". In this way you can easily go back to the excercises without loading the group page again. However, at the bottom of each solution, there is a link that leads you back here.


Depending on the size of your PC-screen or the extend you zoomed in or out of your browser, it might happen that you can see more than one answer for the excercise you worked on. In your own interest, please try not to look at or remember those, if that should be the case.
Depending on the size of your PC-screen or the extent to which you zoomed in or out of your browser, you may see more than one answer per exercise. In your own interest, please try not to look at or remember those, if that should be the case.


Now, have fun with some excercises on quantifiers!
Now, have fun with some excercises on quantifiers!


=== 1. Restricted Quantifiers ===
<span style="color:#00CC00">For further explanation and exercises please have a look at our [http://user.uni-frankfurt.de/~sailer/nmts-wise1213/Quantifiers_Presentation_final.notebook Presentation] and our [http://youtu.be/6c8TwAdvr9U Podcast].</span>
 
 
=== Exercise 1: Restricted Quantifiers===


Find the right formula for the sentence below.
Find the right formula for the sentence below.
Line 98: Line 169:
:: (d) [[SolutionsGroup5#Restricted_Quantifiers_1d|[Some x: STUDENT (x) & INTERVIEW (h, x)] HEAR (x,c)]]
:: (d) [[SolutionsGroup5#Restricted_Quantifiers_1d|[Some x: STUDENT (x) & INTERVIEW (h, x)] HEAR (x,c)]]


<span style="color:red">Comment Sailer:<br />
1) I like this type of exercise. In your example you should use ''the concert'' instead of ''both concerts'', otherwise one might ask oneself where the semantics of the quantifier ''both'' is.<br />
2) instead of saying that the noun phrase must be in the restrictor, you better say that the semantic representation of the NP appears in the restrictor.</span>


=== 2. Different types of Quantifiers ===
=== Exercise 2: Different types of Quantifiers ===


#Which type(s) of Quantifiers has the sentence below?
#Which type(s) of Quantifiers does the sentence below have?
#Write down the corresponding logical formula(s).
#Write down the corresponding logical formula(s).


Line 115: Line 183:
[[SolutionsGroup5#Types_Quantifiers_2d|Check your solution for 2.]]
[[SolutionsGroup5#Types_Quantifiers_2d|Check your solution for 2.]]


<span style="color:red">Comment Sailer: I like this way to give the answers: the user can either click on individual answers or click on the overall answer at the end.
=== Exercise 3: Scopal Ambiguity ===
Remark: in one answer you put "every" (in double quotes) instead of <nowiki>''every''</nowiki> (in two distinct single quotes). Only the latter formatting will  turn into ''every''.</span>
 
=== 3. Scopal Ambiguity ===


# In which way is the following sentence ambiguous?
# In which way is the following sentence ambiguous?
# Write down the two possible logical forms.
# Write down the two possible logical forms.


<span style="color:red">Comment Sailer: Use the normal arrow symbols. Here is how you write them in our wiki: http://www.alanwood.net/unicode/arrows.html
 


'''''Everyone loves someone.'''''
'''''Everyone loves someone.'''''
Line 165: Line 230:


[[SolutionsGroup5#Scopal_Ambiguity_3b|Check your solution for 2.]]
[[SolutionsGroup5#Scopal_Ambiguity_3b|Check your solution for 2.]]
== References and links ==
=== References ===
<!-- Indicate at least 3 references that you will use for your topic -->
* Kearns, Kate (2000): ''Semantics''. New York: St Martin's Press.
* [http://oxforddictionaries.com/definition/english/quantifier?q=quantifier| Definition of quantifier from the Oxford Online Dictionary]
* [http://plato.stanford.edu/entries/generalized-quantifiers/| Definition of quantifier from the Stanford Encylopedia of Philosophy]
*http://grammar.ccc.commnet.edu/grammar/noun_exercise.htm
*http://grammar.ccc.commnet.edu/grammar/determiners/determiners.htm
=== Links ===
<!-- Indicate links that may be helpful for your topic. -->
=== Related Wiki Pages ===
* [[Glossary:_Predicate| Predicate]]
* [[Editing Glossary:Quantifiers| Quantifiers]]
= Our e-learning objects =
== Our wiki pages ==
<!-- List all the wiki pages that were created by your group. -->
=== in the [[Basic Glossary]]: ===
* [[Glossary:Anaphora| Anaphora]]
* [[Glossary:Paraphrase| Paraphrase]]
* [[Glossary:Prototype| Prototype]]
== Our podcasts ==
<!-- List all the podcasts that were created by your group. -->
== Our materials for an interactive whiteboard ==
<!-- List all the files that your group created for the interactive whiteboard. -->


== Our pictures ==
== Our pictures ==
Line 207: Line 237:
File:Me.jpg|Katharina
File:Me.jpg|Katharina
File:Yosemite_National_Park.JPG|Lara
File:Yosemite_National_Park.JPG|Lara
File:Everyone_loves_someone_1.jpeg‎|For exercise scopal ambiguity
File:Everyone loves someone 2.jpeg|For exercise scopal ambiguity
</gallery>
</gallery>
== Our exercises ==
<!-- Provide links to all the exercises that your group has created.-->

Latest revision as of 17:55, 3 April 2016

Warning:
The material on this page has been created as part of a seminar. It is still heavily under construction and we do not guarantee its correctness. If you have comments on this page or suggestions for improvement, please contact Manfred Sailer.
This note will be removed once the page has been carefully checked and integrated into the main part of this wiki.

(Back to the group overview)

Quantifiers (Group 5)

Overview

Members

Short description of the topic

Quantifiers are words that precede and modify nouns; they indicate quantity.

In logic quantification quantifiers bind variables which means that a quantifier connects parts of a sentence which classify a domain of discourse.

There are different types of quantifiers which can be divided in:

  • Universal quantifiers (Logical quantifier)
  • Existential quantifiers (Logical quantifier)
  • Restricted quantifiers

Individual variables are written as "x" and can refer to any individual.


The Universal Quantifier ∀:

  • The Universal quantifier formalizes the notion that something is true for everything, or every relevant thing.
  • Symbol ∀ denotes given any or for all.
  • The sequence "∀x" is read as "For any value of x", "For all values of x" or "Whatever x may be".


The Existential Quantifier ∃:

  • An existential sentence states the existence of at least one thing of the domain.
  • Symbol ∃ stands for noun phrases with a/an, some or there exists sentences.
  • The sequence "∃x" is read as "There is an x" or "There is at least one thing x".


The Restricted Quantifier:

  • Restricted quantifiers point out a proportion of a set, not the proportion of everything there is.
  • Sentences which contain restricted quantifiers are written with square brackets.
  • Examples: some – several – many – most – a few – a number – one/two/three – no – no one – someone – all – every


Scopal Ambiguity:

Scopal ambiguity arises when a sentence contains two or more quantifiers. If this is the case the sentence can be understood in different ways. The difference in meaning can be clarified by expressing the sentence with the corresponding logical formulae. Each of these logical forms represents a particular meaning and thus cannot be ambiguous.


For further explanation and exercises please have a look at our Presentation and our Podcast.


Examples

The Universal Quantifier:

Every dog is barking.

∀x (DOG (x) → BARK (x))

"For every thing x, if x is a dog then x is barking."


The Existential Quantifier ∃:

Some birds were singing.

∃x (BIRD (x) & SING (x))

"There is at least one thing x such that x is a bird and x sings."


The Restricted Quantifier:

Several cars crashed.

[Several x: CAR (x)] CRASH (x)


Scopal Ambiguity:

Some students heard both concerts.

[Some x: STUDENT (x)] [Both y: CONCERT (y)] HEAR (x, y)

"There exist some students such that each of them heard both concerts."

OR

[Both y: CONCERT (y)] [Some x: STUDENT (x)] HEAR (x, y)

"Both concerts were such that each, individually, got heard by some students (but not necessarily the same ones)."

References and Links

References

Links

Definitions in the Basic Glossary:

Our E-Learning Objects

Our Wiki Pages

Definitions in the Basic Glossary:

Our Podcasts

Podcast on Scopal Ambiguity:

Our Materials for an Interactive Whiteboard

Presentation on Quantifiers: Quantifiers.notebook


Our exercises

The following excercises provide links to their respective solutions. The answer to the question you just worked on is shown on the very top of the new website that pops up.

Due to long loading times, it might be useful to open the links via right-click, then choose "Open in new tab". In this way you can easily go back to the excercises without loading the group page again. However, at the bottom of each solution, there is a link that leads you back here.

Depending on the size of your PC-screen or the extent to which you zoomed in or out of your browser, you may see more than one answer per exercise. In your own interest, please try not to look at or remember those, if that should be the case.

Now, have fun with some excercises on quantifiers!

For further explanation and exercises please have a look at our Presentation and our Podcast.


Exercise 1: Restricted Quantifiers

Find the right formula for the sentence below.

Some students who heard the concert were interviewed by Holmes.

(a) [Some x: STUDENT (x)] HEAR (x, c) & INTERVIEW (h, x)
(b) [Some x: STUDENT (x) & HEAR (x, c)] INTERVIEW (h, x)
(c) Some x: STUDENT (x) & HEAR (x, c) & INTERVIEW (h, x)
(d) [Some x: STUDENT (x) & INTERVIEW (h, x)] HEAR (x,c)


Exercise 2: Different types of Quantifiers

  1. Which type(s) of Quantifiers does the sentence below have?
  2. Write down the corresponding logical formula(s).

Ramon signs every sculpture he makes.

(a) existential
(b) universal
(c) restricted

Check your solution for 2.

Exercise 3: Scopal Ambiguity

  1. In which way is the following sentence ambiguous?
  2. Write down the two possible logical forms.


Everyone loves someone.

One Reading
Another Reading

















Check your solution for 1.

Check your solution for 2.

Our pictures