At 3:58 PM +0200 1.9.04, Lutz Strassburger wrote:
> OK, as I suspected, you have a personal, still not very frequent
notion of proof net; my problem was to address the frequent notion
known to the people who frequently ask questions.
OK, I agree with you on the that point. But I still think that you should
reformulate your FAQ entry a little, maybe saying that as most people see
proof nets, the symmetry is only partial, but that there is work in progress
to carry the full symmetry of CoS to PN.
What about:
*** 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). There is yet no notion which flips nets upside-down
and at the same time produces a dual net. On the other hand, we are
working towards bringing the calculus of structures top-down symmetry
to proof nets, so making it possible to deal with nets characterising
derivations, which are more general objects than proofs.
-Alessio
