From: Philip Goetz (philgoetz@gmail.com)
Date: Fri Feb 17 2006 - 08:05:12 MST
On 2/17/06, Marc Geddes <m_j_geddes@yahoo.com.au> wrote:
> Also see blog entry by Ben Goertzel:
>
> *The management of uncertainty in the human brain: new
> experimental insights*
>
> "In other words, some of us maverick AI theorists have
> been saying for a while that using just ONE number
> (typically probability) to measure uncertainty is not
> enough. Two numbers -- e.g. a probability and another
> number measuring the "weight of evidence" in favor of
> this probability (or to put it differently, the
> "confidence" one has in the probability) -- are needed
> to make a cognitively meaningful algebra of
> uncertainty."
I don't know what Ben means by that, since "confidence" in AI is
merely a term that means "this is a number like a probability, but
that does not follow Bayesian rules because my logic engine acts
stupidly if I try that".
But I agree that you need a bunch of numbers, because there are a
bunch of different types of uncertainties that you need to consider.
Consider a field commander told that "Grid section Q32 contains a
defensive formation of twenty tanks". You should be interested in
- Confidence: How certain is the source of their information? This
should be expressed as a probability distribution (for instance, a
mean and a variance), not as a probability.
- Reliability of the information source - Is this coming from
satellite data, or an informant of dubious loyalty?
- Measurement accuracy: How accurate are the sensors used? This
should also be expressed as an error distribution for the sensor,
rather than as a single value. In the example, the question is
whether "40" is an exact number, or an approximation. If it is an
approximation, we might suppose the informant has rounded to the
nearest 10, giving us a uniform distribution from 35 to 44.
- Typicality: In the statement "a defensive formation", how good a
defensive formation is it? This one is hugely important when dealing
with natural language, but has never been made use of.
- Age: When was the observation made?
I did a project back in 2001 or so in which I developed a logic system
that assigned each statement an age and a probability distribution,
rather than a probability. It was obvious, in the domain (fire
prediction), that you needed to assign a probability distribution to
each assertion rather than simply a probability, but again, I'm not
aware of anyone else having done so.
- Phil
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