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".
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.
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".
I agree with this point. A NTV needs a clear interpretation, which is
not a easy job. However, "it is hard to get right" doesn't mean "we'd
better not to use it".
In other words, for the simple statement "birds can fly", the best we can
say is that it may have exceptions.
Well, such a solution is a "safe" one --- easy to justify but doesn't
lead you too far. That is the problem in many AI theories.
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).
Again, there are two languages involved. In a system doing induction,
even if all evidence is binary, the conclusion can (and should) be
multi-valued.
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?
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".
Pei
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