Re: Natural Negations

You can't prove a)? 

Yes, I think that was the original
question of yours, to exhibit a
formula F, which is a classical
tautology, i.e.:

   |-c F

But which cannot be proved in
your special logic with the peirce
axiom (U2) and the contradiction
axiom (U1). i.e.:

  not |-i+U1+U2 F

So that you can show, that |-i+U1+U2
subset |-c is a proper inclusion. Because
of the monotonie of a (natural, etc..)
logic you have:

   |-A F -> |-A,B F

But you can show that B contains
some new information relative to A,
if you can find a formula with:

  not |-A F & |-A,B F

(disclaimer, there are also other
approaches possible)

Bye
.

Relevant Pages

  • Re: Q: Inbetween axiom for NM NJ NK
    ... a simple form of Peirce Law. ... And vice versa, (efq) in NM+: ... Also more and more wondering if f->P is really an axiom of NJ ...
    (sci.logic)
  • Re: Q: Inbetween axiom for NM NJ NK
    ... I wonder whether there is an axiom such that: ... the law of excluded middle in the logic which only uses implication (see ... Thought about the rather unseemingly formula ... How do you prove that Peirce is independent from ...
    (sci.logic)