15.3.1 What's the Problem

Suppose for instance, you want to parse a sentence like

$\mbox{Die schöne nette Frau sieht der kleine Mann}$

The first 5 words of the senctence do not determine whether the noun phrase

$\mbox{die schöne nette Frau}$

is nom_sg_fem or else acc_sg_fem. Only because the noun phrase der kleine Mann is nom_sg_masc it follows that this noun phrase is the subject and hence the other one the object. Thus $\mbox{die schöne nette Frau}$ has to be nom_sg_fem.

the question is now how to process all the disjuctive information about agreements of number, case, and gender. Of course it would be much better to propagate agreement information that enumerate all possible case. For instance, we would like to conjucntion of the following agreement informations:

{ComputeAgree [[sg 2 masc] [pl 3 masc] [pl 3 fem]] [[sg 2 masc] [pl 2 masc] [pl 3 fem] [pl 2 fem]]}

The result should be [[sg 2 masc] [pl 3 fem]].

What we now need is a bijection between a product of finite sets $D_1\times \ldots \times D_n$ and a set of integers of the form $\{0,\ldots,m\}$ . This bijection has to be turned into a bidirectional converter.