On 8/8/06, Pei Wang <[EMAIL PROTECTED]> wrote:
> To assign truth-values (your "probability") to events only is not
> enough for AGI, though you are right that you cannot really assign
> them to universal statements, which are binary by defintion.
>
> To me, the "general statements" (your "implication") in empirical
> science and everyday life are not "universal statements", so can be
> multi-valued. See http://www.cogsci.indiana.edu/pub/wang.induction.ps
> for more.
> To assign truth-values (your "probability") to events only is not
> enough for AGI, though you are right that you cannot really assign
> them to universal statements, which are binary by defintion.
>
> To me, the "general statements" (your "implication") in empirical
> science and everyday life are not "universal statements", so can be
> multi-valued. See http://www.cogsci.indiana.edu/pub/wang.induction.ps
> for more.
I think Richard's point is pertinent here: very often probabilities or NTVs are inappropriate or inapplicable. For example what "birds can fly" really mean in the AGI is "birds can fly, with exceptions". The "exception" is implicit in the nonmonotonic reasoning system. That is the furthest we can go. It's not meaningful to attribute a number to the statement "birds can fly".
Why not? Well, the difficulty is that we cannot come up with a well-defined interpretation of the NTV. For example, we can define the NTV by p = "if you randomly sample a bird in the real world, the chance of it being able to fly". But we can also define p = "if you randomly name a bird species, the chance of that species being able to fly". See? The NTV has got to be
precisely defined, but the additional information required to define it is not contained within the simple statement "birds can fly".
In other words, for the simple statement "birds can fly", the best we can say is that it may have exceptions.
It is far better to assign numbers when the statement has explicit numerical content, eg "the average Chinese person is about 5'7 tall" (I made this up).
So we can always assign numbers explicitly, and avoid assigning NTVs implicitly.
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?
YKY
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