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
--
----------------------------------------------------------------------------
Prof Russell Standish Phone 0425 253119 (mobile)
Mathematics
UNSW SYDNEY 2052
hpcoder@...
Australia
http://www.hpcoders.com.au----------------------------------------------------------------------------
--~--~---------~--~----~------------~-------~--~----~
You received this message because you are subscribed to the Google Groups "Everything List" group.
To post to this group, send email to
everything-list@...
To unsubscribe from this group, send email to
everything-list+unsubscribe@...
For more options, visit this group at
http://groups.google.com/group/everything-list?hl=en-~----------~----~----~----~------~----~------~--~---
