Pei, Ben G. and Abram,
Oh, man, is this stuff GOOD! This is the real nitty-gritty of the AGI
matter. How does your approach handle counter-evidence? How does your
approach deal with insufficient evidence? (Those are rhetorical questions,
by the way -- I don't want to influence the course of this thread, just
want to let you know I dig it and, mostly, grok it as well). I love this
stuff. You guys are brilliant. Actually, I think it would make a good
publication: "PLN vs. NARS -- The AGI Smack-down!" A win-win contest.
This is a rare treat for an old hacker like me. And, I hope, educational
for all (including the participants)! Keep it coming, please!
Cheers,
Brad
Pei Wang wrote:
On Fri, Oct 10, 2008 at 8:03 PM, Ben Goertzel <[EMAIL PROTECTED]> wrote:
Yah, according to Bayes rule if one assumes P(bird) = P(swimmer) this would
be the case...
(Of course, this kind of example is cognitively misleading, because if the
only knowledge
the system has is "Swallows are birds" and "Swallows are NOT swimmers" then
it doesn't
really know that the terms involved are "swallows", "birds", "swimmers" etc.
... then in
that case they're just almost-meaningless tokens to the system, right?)
Well, it depends on the semantics. According to model-theoretic
semantics, if a term has no reference, it has no meaning. According to
experience-grounded semantics, every term in experience have meaning
--- by the role it plays.
Further questions:
(1) Don't you intuitively feel that the evidence provided by
non-swimming birds says more about "Birds are swimmers" than
"Swimmers are birds"?
(2) If your answer for (1) is "yes", then think about "Adults are
alcohol-drinkers" and "Alcohol-drinkers are adults" --- do they have
the same set of counter examples, intuitively speaking?
(3) According to your previous explanation, will PLN also take a red
apple as negative evidence for "Birds are swimmers" and "Swimmers are
birds", because it reduces the "candidate pool" by one? Of course, the
probability adjustment may be very small, but qualitatively, isn't it
the same as a non-swimming bird? If not, then what the system will do
about it?
Pei
On Fri, Oct 10, 2008 at 7:34 PM, Pei Wang <[EMAIL PROTECTED]> wrote:
Ben,
I see your position.
Let's go back to the example. If the only relevant domain knowledge
PLN has is "Swallows are birds" and "Swallows are
NOT swimmers", will the system assigns the same lower-than-default
probability to "Birds are swimmers" and "Swimmers are birds"? Again,
I only need a qualitative answer.
Pei
On Fri, Oct 10, 2008 at 7:24 PM, Ben Goertzel <[EMAIL PROTECTED]> wrote:
Pei,
I finally took a moment to actually read your email...
However, the negative evidence of one conclusion is no evidence of the
other conclusion. For example, "Swallows are birds" and "Swallows are
NOT swimmers" suggests "Birds are NOT swimmers", but says nothing
about whether "Swimmers are birds".
Now I wonder if PLN shows a similar asymmetry in induction/abduction
on negative evidence. If it does, then how can that effect come out of
a symmetric truth-function? If it doesn't, how can you justify the
conclusion, which looks counter-intuitive?
According to Bayes rule,
P(bird | swimmer) P(swimmer) = P(swimmer | bird) P(bird)
So, in PLN, evidence for P(bird | swimmer) will also count as evidence
for P(swimmer | bird), though potentially with a different weighting
attached to each piece of evidence
If P(bird) = P(swimmer) is assumed, then each piece of evidence
for each of the two conditional probabilities, will count for the other
one symmetrically.
The intuition here is the standard Bayesian one.
Suppose you know there
are 10000 things in the universe, and 1000 swimmers.
Then if you find out that swallows are not
swimmers ... then, unless you think there are zero swallows,
this does affect P(bird | swimmer). For instance, suppose
you think there are 10 swallows and 100 birds. Then, if you know for
sure
that swallows are not swimmers, and you have no other
info but the above, your estimate of P(bird|swimmer)
should decrease... because of the 1000 swimmers, you now know there
are only 990 that might be birds ... whereas before you thought
there were 1000 that might be birds.
And the same sort of reasoning holds for **any** probability
distribution you place on the number of things in the universe,
the number of swimmers, the number of birds, the number of swallows.
It doesn't matter what assumption you make, whether you look at
n'th order pdf's or whatever ... the same reasoning works...
From what I understand, your philosophical view is that it's somehow
wrong for a mind to make some assumption about the pdf underlying
the world around it? Is that correct? If so I don't agree with this...
I
think this kind of assumption is just part of the "inductive bias" with
which
a mind approaches the world.
The human mind may well have particular pdf's for stuff like birds and
trees wired into it, as we evolved to deal with these things. But
that's
not really the point. The inductive bias may be much more abstract --
ultimately, it can just be an "occam bias" that biases the mind to
prior distributions (over the space of procedures for generating
prior distributions for handling specific cases)
that are simplest according to some wired-in
simplicity measure....
So again we get back to basic differences in philosophy...
-- Ben G
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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
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