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Russell and Norvig: Chapter 13
CMCS424 Fall 2005
What we call uncertainty is a summary of all that is not explicitly taken into account in the agent’s KB
Very active research field in the 80’s
Non-monotonic logics: defaults, circumscription,
Applications to databases
Default rule: Unless ABF(Tweety) can be proven True, assume it is False
But what to do if several defaults are contradictory?
Which ones to keep? Which one to reject?
We need to answer several questions:
The probability of a proposition A is a real number P(A) between 0 and 1
P(True) = 1 and P(False) = 0
P(AvB) = P(A) + P(B) - P(AB)
Axioms of probabilityNotion of Probability
P(AvA) = P(A)+P(A)-P(A A)
P(True) = P(A)+P(A)-P(False)
1 = P(A) + P(A)So:
P(A) = 1 - P(A)
You drive on Rt 1 to UMD often, and you notice that 70%of the times there is a traffic slowdown at the intersection of PaintBranch & Rt 1.
The next time you plan to drive on Rt 1, you will believe that the proposition “there is a slowdown at the intersection of PB & Rt 1” is True with probability 0.7
There are many situations in which there is no objective frequency interpretation:
P( between 0 and 1CavityToothache)
P(A|B) P(B) between 0 and 1
P(A B) = P(A|B) P(B) = P(B|A) P(A)