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Rushdi Shams, Dept of CSE, KUET, Bangladesh 1
Knowledge Representation
Probabilistic Logic
Artificial Intelligence
Version 2.0
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Rushdi Shams, Dept of CSE, KUET, Bangladesh 2
Conditional Probability
Definition of conditional probability:
P(a | b) = P(a b) / P(b) if P(b) > 0
Product rule gives an alternative formulation:
P(a b) = P(a | b) P(b) = P(b | a) P(a)
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Rushdi Shams, Dept of CSE, KUET, Bangladesh 3
Inference with Probability
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Rushdi Shams, Dept of CSE, KUET, Bangladesh 4
Inference in Probability
P(toothache) =
0.108 + 0.012 + 0.016 + 0.064
= 0.2
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Rushdi Shams, Dept of CSE, KUET, Bangladesh 5
Inference in Probability
P(cavity V toothache) =
0.108 + 0.012 + 0.072 + .008 +
0.016 + 0.064 = 0.28
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Rushdi Shams, Dept of CSE, KUET, Bangladesh 6
Inference in Probability
Can also compute conditional probabilities:
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Rushdi Shams, Dept of CSE, KUET, Bangladesh 7
Inference in Probability
Can also compute conditional probabilities:
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Rushdi Shams, Dept of CSE, KUET, Bangladesh 8
Baye’s Rule
Product rule gives an alternative formulation:
P(a b) = P(a | b) P(b)
= P(b | a) P(a)
Joining them together, we can find-
P(a | b) = P(b | a) P(a)
P(b)
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Rushdi Shams, Dept of CSE, KUET, Bangladesh 9
Application of Bayes’ Rule
A doctor knows that the disease meningitis causes the patient to
have a stiff neck is 50%
Means probability of stiff neck given the probability of having
meningitis
P(s | m) = 0.5
He also knows that in every 50000 patients, 1 may have meningitis
Means probability that a patient has meningitis
P (m) = 1/50000
He also knows that in every 20 patients, 1 may have stiff neck
Means probability that a patient has meningitis
P (m) = 1/20
Then, from Bayes’ rule
P(m | s) = P(s | m) P(m)
P(s)
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Rushdi Shams, Dept of CSE, KUET, Bangladesh 10
Application of Bayes’ Rule
P(m | s) = P(s | m) P(m)
P(s)
= 0.5 X (1/50000)
1/20
= 0.0002
Means he can expect only 1 in 5000 patients with a stiff neck
to have meningitis
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Rushdi Shams, Dept of CSE, KUET, Bangladesh 11
References
Artificial Intelligence: A Modern Approach (2nd
Edition)
by Russell and Norvig
Chapter 13
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