On Feb 7, 2007, at 4:35 PM, gts wrote:
On Wed, 07 Feb 2007 16:07:13 -0500, Ben Goertzel <[EMAIL PROTECTED]>
wrote:
only under an independence assumption.
True, I did not make the independence assumption explicit.
Note that dutch books cannot be made against an AGI that does not
claim to have knowledge it does not have.
That is true and important, and is why Pei and I and others use
multiple-component truth values in our systems -- we explicitly
track the weight of evidence associated with uncertainty estimates.
I don't see how multiple-component truth values might block a fully
developed Novamente from being vulnerable to dutch books, if that
is what you are saying here.
What confidence (weight of evidence) assessment does is makes the
system smarter about when it knows a lot and when it doesn't know a lot.
This would not help it, if it were forced into de Finetti style dutch
book situations. In a situation like that, you have to name a price
no matter how ignorant you may be --- so if you have zero knowledge
about the subject of the bet, you have to make up a random price. If
you have very little knowledge about the subject of the bet, you have
to make up a price in which you have extremely little confidence.
But it helps the system in real-world situations, which do not
consist of de Finetti style dutch book situations, by and large.
In the Novamente (indefinite probabilities) approach, multiple-
component truth values are ultimately all about time. The system has
its probability assessment now, which may be well-grounded or may be
almost arbitrary or truly arbitrary if it has little or no
information. Then, it has its probability assessment of what its
probability assessment is likely to be in the future, once it has
more information. The more evidence it has about a phenomen, in
general, the more accurately it can constrain its future probability
assessments regarding the phenomenon based on its prior knowledge.
So, the indefinite probabilities **are** probabilities, they don't go
outside the probabilistic framework, but they are useful
probabilities about the system's own expected actions in the future.
In a casino full of different dutch book opportunities, they would
help the system figure out which dutch book opportunities to avoid
(the ones where the system is least certain about its future
probability estimates). But of course one could also force the
system into dutch book games regarding its choices of which dutch
book games to avoid, etc.
In fact I have been thinking about how one might attempt a dutch
book against Novamente involving your multiple component values,
but I do not yet fully understand b. My impression at the moment is
that b is similar to 'power' in conventional statistics -- a real
number from 0 to 1 that roughly speaking acts as a measure of the
robustness of the analysis. Fair comparison?
The power of a statistical hypothesis test measures the test's
ability to reject the null hypothesis when it is actually false ...
this has very little to do with indefinite or imprecise probabilities...
-- Ben
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