Tree of numbers

From Glottopedia
Jump to navigation Jump to search

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.
STUB
CAT This article needs proper categorization. You can help Glottopedia by categorizing it
Please do not remove this block until the problem is fixed.