Difference between revisions of "Tree of numbers"

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In a sentence of the form [<sub>S</sub> [<sub>NP</sub> D CN] VP] the set A of entities denoted by the common noun CN can be divided into a subset with elements that belong to the set B of entities represented by VP, and a subset with elements that don't belong to that set, i.e. A intersect B and A - B, respectively. In a domain with n dogs, the dogs can be divided over these two subsets in n+1 ways, each of which is represented by an ordered pair x,y where x = |A intersect B| and y = |A - B|. The tree of numbers is a complete representation of all these pairs of numbers for each possible size of A:
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==Definition==
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In a sentence of the form [<sub>S</sub> [<sub>NP</sub> D CN] VP] the set A of entities denoted by the common noun CN can be divided into a subset with elements that belong to the set B of entities represented by VP, and a subset with elements that don't belong to that set, i.e. A intersect B and A - B, respectively. In a domain with n dogs, the dogs can be divided over these two subsets in n+1 ways, each of which is represented by an ordered pair x,y where x = |A intersect B| and y = |A - B|.  
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==Examples==
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The tree of numbers is a complete representation of all these pairs of numbers for each possible size of A:
  
 
  (i) |A|=0       0,0
 
  (i) |A|=0       0,0
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Many properties of determiners (like [[upward monotonicity]] and [[downward monotonicity]]) and relations between determiners (like negation) can be clarified in the tree of numbers.
 
Many properties of determiners (like [[upward monotonicity]] and [[downward monotonicity]]) and relations between determiners (like negation) can be clarified in the tree of numbers.
  
=== Links ===
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== Links ==
 
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*[http://www2.let.uu.nl/UiL-OTS/Lexicon/zoek.pl?lemma=Tree+of+numbers&lemmacode=191 Utrecht Lexicon of Linguistics]
[http://www2.let.uu.nl/UiL-OTS/Lexicon/zoek.pl?lemma=Tree+of+numbers&lemmacode=191 Utrecht Lexicon of Linguistics]
 
  
 
=== References ===
 
=== References ===
 
 
* Gamut, L.T.F. 1991. ''Logic, language, and meaning,'' Univ. of Chicago Press, Chicago.
 
* Gamut, L.T.F. 1991. ''Logic, language, and meaning,'' Univ. of Chicago Press, Chicago.
  
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[[Category:Semantics]]
 
[[Category:Semantics]]
  
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Latest revision as of 07:35, 30 August 2014

Definition

In a sentence of the form [S [NP D CN] VP] the set A of entities denoted by the common noun CN can be divided into a subset with elements that belong to the set B of entities represented by VP, and a subset with elements that don't belong to that set, i.e. A intersect B and A - B, respectively. In a domain with n dogs, the dogs can be divided over these two subsets in n+1 ways, each of which is represented by an ordered pair x,y where x = |A intersect B| and y = |A - B|.

Examples

The tree of numbers is a complete representation of all these pairs of numbers for each possible size of A:

(i) |A|=0		       0,0
    |A|=1		    1,0   0,1
    |A|=2		 2,0   1,1   0,2
    |A|=3	      3,0   2,1	  1,2	0,3
    |A|=4          4,0   3,1   2,2   1,3   0,4
    |A|=5       5,0   4,1   3,2   2,3	1,4   0,5
    ...	 		       ...

The meaning of a determiner D can be represented as a subset of a tree of numbers. The determiner every, for example corresponds to the x,0 pairs on each row:

(ii) |A|=0		  +
     |A|=1	      +	     -
     |A|=2	   +  	  -	 -
     |A|=3	+     -	      -	    -
     ...		 ...

Many properties of determiners (like upward monotonicity and downward monotonicity) and relations between determiners (like negation) can be clarified in the tree of numbers.

Links

References

  • Gamut, L.T.F. 1991. Logic, language, and meaning, Univ. of Chicago Press, Chicago.
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