On Sun, Feb 15, 2009 at 06:41:08PM +0100, Bruno Marchal wrote:
> >>
> >> A good and important exercise is to understand that with the Kripke
> >> semantics,  ~Dt, that is B~t, that is Bf, that is "I prove 0=1", is
> >> automatically true in all cul-de-sac world. It is important because
> >> cul-de-sac worlds exists everywhere in the Kripke semantics of the
> >> self-reference logic G.
> >>
> >> If you interpret, if only for the fun, the worlds as state of life,
> >> then Bf is  really "I am dead".
> >>
> >> Bruno
> >
> > Yes, but I have difficulty in _simultaneously_ interpreting logic
> > formulae in terms of Kripke frames and B as provability. In the
> > former, Bp means in all successor worlds, p is true, whereas in the
> > latter it means I can  prove that p is true.
> >
> > How does one reconcile such disparate notions?
> 
> 
> By Godel's theorems, Löb's theorems and Solovay theorems.
> 

...

The following snip did not answer my question on how one can
simultaneously have Kripke semantics and provability semantics. Never
mind.

I'm helping Kim Jones with the translation - maybe it'll make more
sense when we get to that bit.

Cheers
-- 

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Prof Russell Standish                  Phone 0425 253119 (mobile)
Mathematics                              
UNSW SYDNEY 2052                         hpco...@hpcoders.com.au
Australia                                http://www.hpcoders.com.au
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