 In fact I found that your formalization would gain if it will be
some more complex; The way in which I try to expose this to you was also a
big reduction. The better is to look at Culioli formalization :

Culioli A. (1995). Cognition and representation in linguistic theory.
Amsterdam, J.Benjamins.
  
It is the same thing for determination :  I believe that it is the same
thing as you, but I am in the habit of seeing it more formalized, or more
exactely in a different way (cf Culioli). The way I explained y