Re: Help with a problem

On Sat, 26 Nov 2005 03:19:24 -0800, William Elliot
<marsh@xxxxxxxxxxxxxxxxxx> wrote:

> >
> > a comparison:
> >
> Vivid. Also pin points the places where equivalence needs be shown.
>
Right.

> >
> > Gentzen W. Elliot Name (Gentzen)
> > -----------------------------------------------------
> >

> >
> > [A] [B]
> > : : A -> C
> > A v B C C B -> C
> > -------------- ----------- vE
> > C A v B -> C
> >

It's easy to show that both rules are "equivalent" (in the presence of
->I and ->E), though *I* would prefer Gentzen's rule in a system of ND.

Note that a synthesis of those two rules is also possible:

A v B, A -> C, B -> C
--------------------- (vE)
C

> >
> > A ~A ~A
> > ------- ------ ~E
> > _|_ A -> f
> >

Again, it's easy to show that both rules are "equivalent", assuming that
we have _|_ = f. (It's clear that f and _|_ have the same function in
both systems.)

> >
> > [A]
> > :
> > _|_ A -> f
> > ----- ------ ~I
> > ~A ~A
> >

Same, same...


F.

--
"I do tend to feel Hughes & Cresswell is a more authoritative
source than you." (D. Ullrich)
.

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