I'm considering nonmonotonic reasoning using Bayes net, and got stuck.
There is an example on p483 of J Pearl's 1988 book PRIIS:
Given:
"birds can fly"
"penguins are birds"
"penguins cannot fly"
The desiderata is to conclude that "penguins are birds, but penguins
cannot fly".
Pearl translates the KB to:
P(f | b) = high
P(f | p) = low
P(b | p) = high
where high and low means arbitrarily close to 1 and 0, respectively.
If you draw this on paper you'll see a triangular loop.
Then Pearl continues to deduce:
Conditioning P(f | p) on both b and ~b,
P(f | p) = P(f | p,b) P(b | p) + P(f | p,~b) [1-P(b | p)]
> P(f | p,b) P(b | p)
Thus
P(f | p,b) < P(f | p) / P(b | p) which is close to 0.
Thus Pearl concludes that "given penguin and bird, fly is not true".
But I found something wrong here. It seems that the Bayes net is
loopy and we can conclude that "fly" given "penguin" and "bird" can be
either 0 or 1. (The loop is somewhat symmetric).
Ben, do you have a similar problem dealing with nonmonotonicity using
probabilistic networks?
YKY
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agi
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