Re: Answer "how to prove ~(P <--> Q) |- ~P <-->Q "

On Sat, 02 Jun 2007 10:33:57 -0000, translogi
<wilemien@xxxxxxxxxxxxxx> wrote:


The only shortcomings (as i see them) are the ~E rule
(It is anti-intuitionistic, Why not have a bit more proper ~~E rule?
At least smart students will grasp there is something wrong with ~E )

I see. Though you know that the symmetry of I and E rules is broken
for '~' if we do not use the logical primitive '_|_' (for "the
false statement") like Gentzen did. (That's a difficulty ALL those
systems have to deal with.)


And the way you say that an assumption is decharged [...]

Yes. Same with me. Actually, I like Lemmon's simple notation (which
is just straightforward).


But these are minor points

Sure.


The use of DS (disjunctive syllogism) instead of vE is a good thing,

Nope. I don't think so. IMHO it's rather a very bad idea. :-(

It breaks the symmetry of Gentzen's original rules of derivation
without necessity (this time for 'v').


it brings logic back to the Stoic undemonstratebles that also has
DS.

Well, it's no problem to use DS as a _derived_ rule in, say,
Lemmon's system.


F.

--

E-mail: info<at>simple-line<dot>de
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