At 16:20 +0200 31.8.04, Lutz Strassburger wrote:
On Tue, 31 Aug 2004, Alessio Guglielmi wrote:
> I don't understand your remark. Take
+----+ +----+
| | | |
a -a a -a
\ | | /
\ +---+ / .
\ /
\ /
\ /
a P -a
How am I supposed to turn around this?
like this:
-a P a
/ \
/ \
/ \
/ +---+ \
/ | | \
-a a -a a
| | | |
+----+ +----+
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.
As a side remark, I would say: with super-symmetries come
super-responsibilities (like for Marvel super-heroes). Flipping a
proof net and getting a refutation net is trivial; after you do this,
you should also feel the moral obligation of talking about
*derivation* nets, meaning top-down symmetric objects with non-unit
premise and conclusion. They represent the natural closure of the
symmetry you're talking about. And then: what is a correct derivation
net? Do you have a correctness criterion, sequentialisation, etc.?
What I mean is that a `correct point of view' should be productive in
some technical sense. I guess we agree, but I still don't see the
practical benefits of your point of view.
-Alessio
