Re: Two more FAQ entries

On Saturday 28 August 2004 19:53, Alessio Guglielmi wrote:
> Hi,
>
> it's me again. Two more entries for the FAQ, please comment. In
> general, do you have any complaint or suggestion for the FAQ page?
>
> -Alessio
>
>
> *** Question   Aren't proof nets top-down symmetric objects, not
> differently than proofs in the calculus of structures?
>
> *** Answer   No, proof nets are top-down asymmetric: they consist of
> trees with some links on top (in the simplest case of multiplicative
> linear logic). If you flip a proof net upside-down, you don't get a
> dual proof net, just an upside-down one.

Alessio,

I do not (entirely) agree on this point. The problem is that proof nets are 
usually drawn the wrong way (ie assymmetric). But actually, they are 
symmetric: If you take for example a PN (say for MLL) with two conclusions A 
and B, then you can draw that object with the two conclusions down and the 
links above (the usual way), or you can draw it with A on top and B at the 
bottom and the links in between, or the other way arround, or both formulas 
at the top, and all the links at the bottom.
The only important point is that we do not get a "dual proof net", but the 
same proof net. Maybe that is the real difference: if you take a CoS 
derivation an its dual, they yield the same proof net.

-Lutz