YKY,
It is inevitable to be vacillating at the beginning. It will be fine
as long as you don't begin to build the system before your design is
relatively stable.
I don't think predicate logic plus probability is the way to go, but
won't try to convince you by email. I've said more in my writings.
Of course NARS can express much more than just "P is Q". I mentioned that in
http://www.cogsci.indiana.edu/farg/peiwang/PUBLICATION/wang.cognitive_mathematical.pdf
and gave more details in my other publications, as well as the demo
examples.
Pei
On 8/10/06, Yan King Yin <[EMAIL PROTECTED]> wrote:
On 8/9/06, Pei Wang <[EMAIL PROTECTED]> wrote:
> There are two different issues: whether an external communication
> language needs to be multi-valued, and whether an internal
> representation language needs to be multi-valued. My answer to the
> former is "No", and to the latter is "Yes". Many people believe that
> since we usually don't attach numbers to our sentences, there is no
> point to use it within an AGI system. I don't think so, and I've
> mentioned previously why I think nonmonotonic logic cannot support
> AGI.
Sorry that my view on this is vacillating. Now I think assigning NTV
universally to all sentences (in the internal representation) is OK. Also I
think the NTVs can be Bayesian (subjective) probabilities.
To avoid confusion we can fix it that the probability/NTV associated with a
sentence is always interpreted as the (subjective) probability of that
sentence being true.
So p( "all ravens are black" ) will become 0 whenever a single nonblack
raven is found.
If, from experience, 99% of ravens are black (maybe some are painted white),
we can assign p ( "the random raven being black" ) = 0.99.
This resolves the problem of sentence-level and sub-sentential
probabilities.
This does not resolve Hempel's paradox yet. I think it's a matter of
heuristics. Bayesians think a nonblack nonraven contributes infinitesimally
to p( "all ravens are black" ). Numerically it does not make a big
difference.
> > A further example is:
> > S1 = "The fall of the Roman empire is due to Christianity".
> > S2 = "The fall of the Roman empire is due to lead poisoning".
> > I'm not sure whether S1 or S2 is "more" true. But the question is how
can
> > you define the meaning of the NTV associated with S1 or S2? If we
can't,
> > why not just leave these statements as non-numerical?
>
> If you cannot tell the difference, of course you can assign them the
> same value. However, very often we state both S1 and S2 as "possible",
> but when are forced to make a choice, can still say that S1 is "more
> likely".
After some reflection I think it is sensible to assign degrees of belief
(probabilities) to those statements. What we need is a systematic way of
dealing with p/NTVs during all possible inference steps. My guess is to
combine predicate logic with Bayesian probabilities. I agree that Bayesian
conditionalization alone is insufficient for an AGI's learning.
Popper's paradox (see below) can be resolved by the AGI's episodic memory
(if it remembers that p = 0.5 is obtained from experiment). So we don't
need to put all information in one sentence.
I assume that NARS provides a reasonable alternative way of assigning NTVs.
But NARS uses term logic which is only capable of expressing things like "P
is Q". I think AGI needs the expressiveness of predicate logic? Why not
use NARS-style <f,c> in predicate logic?
Appendix: from
http://www.wutsamada.com/alma/phlsci/ohear7.htm
=================================
Popper's Paradox of Ideal Evidence
suppose we have a coin and our subjective interpretation says it has a .5
probaility it will come up heads
meaning we are 50% ignorant of how it will turn up.
suppose we have conducted a long string of tosses with a distribution
approaching 50/50
we have learned nothing: we're still 50% ignorant
but we have learned something about the coin; that the probability of heads
really is .5; it's a fair coin
YKY ________________________________
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