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: | + | ==Definition== |
| + | 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|. | ||
| + | |||
| + | ==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 | (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 == | |
| − | + | *[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. | ||
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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