This seems loosely related to the ideas in 5.10.6 of the PLN book, "Truth
Value Arithmetic" ...
ben
On Fri, Oct 10, 2008 at 9:04 PM, Abram Demski <[EMAIL PROTECTED]> wrote:
> On Fri, Oct 10, 2008 at 4:24 PM, Ben Goertzel <[EMAIL PROTECTED]> wrote:
>
> >> Given those three assumptions, plus the NARS formula for revision,
> >> there is (I think) only one possible formula relating the NARS
> >> variables 'f' and 'w' to the value of 'par': the probability density
> >> function p(par | w, f) = par^(w*f) * (1-par)^(w*(1-f)).
> >
> > Why is this the only possible formula?
>
> Let's see... let's call the function we're looking for L(f,w). To
> satisfy NARS revision it must have the property L(f1,w1)*L(f2,w2)=L{
> (w1*f1+w2*f2)/(w1+w2) , w1+w2 }. Taking f1=f2 and w1=w2, we have:
>
> L(f,w)^2=L{ (2*w*f)/(2*w) , 2*w}
> L(f,w)^2=L{ f, 2*w}
>
> That establishes that the function is exponential in w, but that's a
> far cry from proving the uniqueness of the formula I gave. I should
> not have asserted so boldly...
>
> --Abram
>
>
> -------------------------------------------
> agi
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--
Ben Goertzel, PhD
CEO, Novamente LLC and Biomind LLC
Director of Research, SIAI
[EMAIL PROTECTED]
"Nothing will ever be attempted if all possible objections must be first
overcome " - Dr Samuel Johnson
-------------------------------------------
agi
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