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

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


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

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