On Fri, Feb 13, 2009 at 07:31:29PM +0100, Bruno Marchal wrote:
> >
> > I'm a little confused. Did you mean Dp here? Dp = -B-p
> Fair question, given my sometimes poor random typo!

> deduce Bp) , well, if you remind the definition of the Kripke  
> semantics, you can see that
> Bp & Dp
> is equivalent with
> Bp & Dt

> Now if you have in a world, your world if you want,  Bp & Dp, you have  
> at least access to a world in which p is true, and thus you have  
> access to a world where t is true, given that t is true in all worlds.  
> So you have Bp & Dt.

Thanks. Alles ist Klar. I think I wasn't taking seriously enough the
idea of Kripke frames before...


> 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?


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

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