Tree of numbers - Revision history

NBlöcher: Removed the block {{format}}

2014-08-30T07:35:32Z

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Wohlgemuth: utrecht

2009-06-10T12:09:35Z

utrecht

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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:

(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 ===

[http://www2.let.uu.nl/UiL-OTS/Lexicon/zoek.pl?lemma=Tree+of+numbers&lemmacode=191 Utrecht Lexicon of Linguistics]

=== References ===

* Gamut, L.T.F. 1991. ''Logic, language, and meaning,'' Univ. of Chicago Press, Chicago.

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[[Category:Semantics]]

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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:
+==Definition==
   (i) |A|=0		       0,0
@@ Line 19: / Line 23: @@
 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 ===
+== Links ==
+*[http://www2.let.uu.nl/UiL-OTS/Lexicon/zoek.pl?lemma=Tree+of+numbers&lemmacode=191 Utrecht Lexicon of Linguistics]
 === References ===
 * Gamut, L.T.F. 1991. ''Logic, language, and meaning,'' Univ. of Chicago Press, Chicago.