[P1] ================================================ AMAST Links 02 04

            What are categorical models of logics good for?
            by _Greg Restall_ <Greg.Restall@cisr.anu.edu.au>

   The up-to-date _full record of the discussion_ about this question
   in the Linear Forum is available as a plain-text file at URL:
   http://www.cs.utwente.nl/data/amast/links/v02/i04/full/AC0204P1.txt
   Further related work may be found through the following WWW pages:
   Greg Restall : http://arp.anu.edu.au/arp/gar/gar.html
   Uday S Reddy : http://vesuvius.cs.uiuc.edu:8080/home/reddy.html

  I've read with interest the discussion of categorical models of
linear logics.  I've wrapped my brain around the recent results, and
I've enjoyed it immensely.  I do have a question about categorical
models, however, and I think that this list is as good a place as any
to have them answered.  My question is this.  
   What are categorical models of logics good for?
Possible answers are as follows.
 1. They help us understand our term assignment systems for these
    logics.
 2. They help us prove results about our logics, as we can use category
    theory.
 3. We can show that our favourite logic corresponds to some
    already-found structure in category theory, and hence, our logic 
    gets brownie-points for being `natural.'
 4. The category (or class of categories) we are interested in is the
    *intended model* for our logic.  That is, we are using our logic
    to model some phenomenon, which we have already presented
    categorically.  As we have shown that this category (or class of
    categories) is a model of our logic, we thereby show that our logic
    models nicely the phenomenon of interest.
  Are any of these answers correct?  If so, which of them?  Or are they
missing the point?  Are categorical models interesting for some other
reason? I'd be very interested if there are any results like those
foreshadowed in answer `4' actually appear in the literature on linear 
logic.  The most I can find is answers in the ballpark of 1, 2 and
maybe 3.  
  Replies can be sent to the list, or to me.  Either is fine.