1. Artificial Intelligence
Version 1.0
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2. Two gambles
 we bet on a head turning up when we toss a coin that is
known to be fair
 we bet on the outcome of a fight between the world's
greatest boxer and the world's greatest wrestler.
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3. Why DST
 If we have absolutely no information about the coin, in
probability theory,
 we will assume that it would be 50% head and 50% tail
 we know the coin is fair, so we know for a fact that
 it would be 50% head and 50% tail.
 Therefore, in the two different scenarios,
 we arrive at the same conclusion.
 How we present total ignorance in probability theory
becomes a problem.
3RS, CSE@KUET

4. Why DST
 In Dempster–Shafer Theory,
 for the ignorance scenario,
 the belief of Head and the belief of Tail would be 0.
 For the fair coin scenario,
 the belief of Head would be 0.5, the belief of Tail would also
be 0.5.
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5. Formalism
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6. Formalism
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7. Formalism
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8. Effects of conflict (Low Conflict)
 Suppose that one doctor believes a patient has
 either a brain tumor — with a probability of 0.99
 or meningitis — with a probability of only 0.01.
 A second doctor also believes the patient has
 a brain tumor — with a probability of 0.99
 and believes the patient suffers from concussion — with
a probability of only 0.01.
 If we calculate m (brain tumor) with Dempster’s
rule, we obtain m(brain tumor)=Bel (brain tumor)=1
8RS, CSE@KUET

9. Effects of conflict (High Conflict)
 Suppose that one doctor believes
 a patient has either meningitis with a probability of
0.99
 or a brain tumor with a probability of only 0.01.
 A second doctor believes
 the patient suffers from concussion with a probability of
0.99
 and also believes the patient has a brain tumor with a
probability of only 0.01.
 If we calculate m (brain tumor) with Dempster’s
rule, we obtain m(brain tumor)=Bel (brain tumor)=1
9RS, CSE@KUET

10. Belief and Plausibility
 Shafer's framework allows for belief about propositions
to be represented as intervals, bounded by two
values, belief (or support) and plausibility:
belief ≤ plausibility.
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11. Belief and Plausibility
 Suppose we have a belief of 0.5 and a plausibility of 0.8
for a proposition, say “the cat in the box is dead.” This
means that we have evidence that allows us to state
strongly that the proposition is true with a confidence
of 0.5. However, the evidence contrary to that
hypothesis (i.e. “the cat is alive”) only has a confidence
of 0.2. The remaining mass of 0.3 (the gap between the
0.5 supporting evidence on the one hand, and the 0.2
contrary evidence on the other) is “indeterminate,”
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12. Belief and Plausibility
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13. Belief and Plausibility
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14. Belief and Plausibility
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15. Belief and Plausibility
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16. Belief and Plausibility
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17. Belief and Plausibility
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18. Belief and Plausibility
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19. Belief and Plausibility
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20. Belief and Plausibility
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21. Belief and Plausibility
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22. 22RS, CSE@KUET

23. 23RS, CSE@KUET

24. 24RS, CSE@KUET

25. 25RS, CSE@KUET

26. 26RS, CSE@KUET

27. 27RS, CSE@KUET

28. 28RS, CSE@KUET

29. References
 Wikipedia, http://en.wikipedia.org/wiki/Belief_functi
ons
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30. Stole few slides from
 Miguel Garcia Remesal, mgremesal@fi.upm.es
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