On Feb 7, 2007, at 3:48 PM, gts wrote:
Ben,
Of course the world is an enormously complex relation of
interdependencies between many causes and effects. I do not dispute
that fact.
I question however whether this should really be an important
consideration in developing AGI.
One's probabilistic judgements should always be justified, yes? And
when a probabilistic judgement P(A) is justified only by one or
more other probabilistic judgements [P(Q), P(R), and P(S), say]
then one is not justified in assuming P(A) should have a value
greater than [P(Q) * P(R) * P(S)]. Yes?
Well, if
A = Q and R and S
then
P(A) = P(Q) * P(R) * P(S)
only under an independence assumption.
If Q=R, but S is independent of R, then we have
P(A) = P(Q) * P(S)
which is generally bigger than
P(Q) * P(R) * P(S)
More commonly, if Q, R and S have some dependencies but are not
identical, then we'll find
P(A) > P(Q) * P(R) * P(S)
The problem is that calculating the dependencies accurately, if Q, R
and S are complex entities themselves,may require more resources than
the mind in question (human or AI) has available.
If that coherency condition is not true for an AGI then I might
have trouble trusting its probabilistic judgements. I do not much
care in this case whether our AGI is correct in its probabilistic
judgement about A (it may be ignorant about many facts of the world
including many facts related to judgements about Q, R and S) but I
do care whether our AGI is *justified* in its appraisal of P(A).
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.
But knowing what knowledge you have (weight of evidence assessment)
is **also** a problem that a moderate-resources mind cannot solve
exactly. For instance, there is the issue of estimating the
independence or otherwise between two different pieces of evidence,
which is needed to do accurate evidence-counting...
-- Ben
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