Linear Logic Maybe

From: Jan Burse (janburse_at_fastmail.fm)
Date: 02/09/05 

Date: Thu, 10 Feb 2005 00:27:50 +0100

Dear All

I am working on an algebra for some
language processing. The language
processing includes the combination
of nouns, verbs and adjectives.

So I came up first with the
following connectives:

   A & B: Conjunction
   A v B: Disjunction

And some rules, for example
disjunctive normal form:

   A & (B v C) --> (A & B) v (A & C)
   etc..

This works pretty well for some
language phaenomena. For example
"roof, window and door", kann be
modeled by &, and so on.

Now I was introducing the following
two connectives:

    A ! B: Composition
    A ? B: Guard

And the rules are as such:

    A ! (B ! C) --> (A ! B) ! C
    (A & B) ! C --> A ! C & B ! C (i)
    A ! (B & C) --> A ! B & A ! C (ii)
    etc..
    (A ? B) ! C --> (B ! A) & (B ! C) (iii)
    etc..

This works pretty well for some
language phaenomena. For example
"the green door is open" can be
modelled by (green?door)!open.

But now, as I dont have any clue
what algebra this might be, so that
I can lookup up the algebras properties,
many questions arise. For example

1) Does the order of application
    of the rules (i) and (ii) make
    any difference in the normal form?
    (answer = yes, guess why?)

2) Similar questions in the interaction
    between ? and !, not yet answered
    for my self.

Any pointers welcome?

Best Regards 

---
Spuntik III

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