Numerical Repr of Uncertainty

• Probability

  • Our state of knowledge about the world is a distribution of the form prob(s), where s is the set of all states
    • 0 <= prob(s) <= 1 for all s
    • ?S prob(s) = 1
    • For subsets S1 and S2, prob(s1 ? S2) = prob(s1) + prob(s2) - prob(s1 ? S2)
    • Note we can equivalently talk about propositions:prob(p ? q) = prob(p) + prob(q) - prob(p ? q)

• Interval-based methods

  • .4 <= prob(p) <= .6

• Fuzzy methods

  • D(tall(john)) = 0.8

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