Re: Splitting for classical logic

On Tue, 5 Oct 2004, Alessio Guglielmi wrote:

> Speaking of which: there wasn't much time to discuss because Lutz had 
> to leave, so perhaps we can do so on the list. Lutz has a splitting 
> proof for classical logic, but for a different system than KS (no 
> medial, in particular). I don't think this solves the problem as I 
> stated it, because if we have to look for general criteria, we 
> probably want to deal with medial, since this rule pops up so often, 
> also in completely unrelated systems and in different shapes, like 
> unary versions for classical logic. But let's discuss the pros and 
> cons.

Alessio,

Sorry, your mail was too long. I did not get what you mean by 
 
  "the problem as I stated it"

I know that for proving my splitting I deliberately avoid medial, but as a 
corollary you get splitting for KS in a very strong way. You also get it 
for the system {ai_, s, m}, which means that there is no additional 
weakening or contraction. My method of putting medial into some super-rule 
realizes exactly the idea that Elaine tried to explain after Roy found the 
bug in your proof.
Of course, since splitting holds for {ai_, s, m}, there might also be a 
direct proof, without using the super-rule, but it is most like going 
to be quite messy. 

Ciao,
Lutz