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 -- *PS: A number of people ask me about the attachment to my email, which is of type "application/pgp-signature". Don't worry, it is not a virus. It is an electronic signature, that may be used to verify this email came from me if you have PGP or GPG installed. Otherwise, you may safely ignore this attachment. ---------------------------------------------------------------------------- A/Prof Russell Standish Phone 8308 3119 (mobile) Mathematics 0425 253119 (") UNSW SYDNEY 2052 [EMAIL PROTECTED] Australia http://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 ----------------------------------------------------------------------------
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