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billswift comments on Deleting paradoxes with fuzzy logic - Less Wrong
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I don't understand this statement: "p(AvB) >= p(A^B), when Bayes' law just blows up".
p(AvB) >= p(A^B) should always be true shouldn't it?
I know A^B -> AvB is a tautology (p=1) and that the truth value of AvB -> A^B depends on the values of A and B; when translated into probabilities show p(AvB) >= p(A^B) as true.
If you're told p(A|B) = 1, but are given different values for p(A) and p(B), you can't apply Bayes' law. Something you've been told is wrong, but you don't know what.
Note that the fuzzy logic rules given are a compromise between A and B having correlation 1, and being independent.