On Mon, Dec 05, 2005 at 03:58:20PM +0100, Bruno Marchal wrote:
> >
> >Well at least this isn't a problem of translation. But I still have
> >difficulty in understanding why Pp=Bp & -B-p should be translated into
> >English as "to bet on p" (or for that matter pourquoi on devrait
> >le traduire par "a parier a p")
> >
> >For me Bp & -B-p is simply a statement of consistency - perhaps what
> >we mean by mathematical truth.
> 

...

> So "probability of p (in world alpha) is equal to one" is well captured 
> by Bp&Dp (in world alpha).  This means (Kripke-semantically) "p is true 
> in all accessible world & there is at least one possible world where 
> true is false".

...
> 
> Tell me if this is clear enough. Euh I hope you agree that "To bet on 
> p" can be used for the probability one, of course. If that is the 
> problem, remember I limit myself to the study of the "probability one" 
> and its modal dual "probability different from zero".
> 
> I must go now and I have not really the time to reread myself, hope I 
> manage the "s" correctly. Apology if not. Please ask any question if I 
> have been unclear.
> 
> Bruno
> 
> 
> http://iridia.ulb.ac.be/~marchal/

Yes - this does make sense. Kripke frames are a good way of explaining
why Bp&Dp captures prob=1 type statements. I'm still not sure "bet
on" is the correct verb though, as in normal life one bets on things with
prob <1 (eg on a horse winning a race). Prob=1 is a "sure bet", but I
can't quite think of an appropriate verb.

Cheers

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