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?

Cheers
-- 

----------------------------------------------------------------------------
Prof Russell Standish                  Phone 0425 253119 (mobile)
Mathematics                              
UNSW SYDNEY 2052                         hpco...@hpcoders.com.au
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-l...@googlegroups.com
To unsubscribe from this group, send email to 
everything-list+unsubscr...@googlegroups.com
For more options, visit this group at 
http://groups.google.com/group/everything-list?hl=en
-~----------~----~----~----~------~----~------~--~---

Reply via email to