Your SlideShare is downloading. ×
Upcoming SlideShare
Loading in...5
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×

# Saving this for later?

### Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime - even offline.

#### Text the download link to your phone

Standard text messaging rates apply

# Probabilistic logic

123
views

Published on

Published in: Education, Technology

0 Comments
0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
Your message goes here
• Be the first to comment

• Be the first to like this

No Downloads
Views
Total Views
123
On Slideshare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
Downloads
6
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

### Transcript

• 1. Rushdi Shams, Dept of CSE, KUET, Bangladesh 1 Knowledge Representation Probabilistic Logic Artificial Intelligence Version 2.0
• 2. 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)
• 3. Rushdi Shams, Dept of CSE, KUET, Bangladesh 3 Inference with Probability
• 4. Rushdi Shams, Dept of CSE, KUET, Bangladesh 4 Inference in Probability  P(toothache) = 0.108 + 0.012 + 0.016 + 0.064 = 0.2
• 5. 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
• 6. Rushdi Shams, Dept of CSE, KUET, Bangladesh 6 Inference in Probability  Can also compute conditional probabilities:
• 7. Rushdi Shams, Dept of CSE, KUET, Bangladesh 7 Inference in Probability  Can also compute conditional probabilities:
• 8. 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)
• 9. 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)
• 10. 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
• 11. Rushdi Shams, Dept of CSE, KUET, Bangladesh 11 References  Artificial Intelligence: A Modern Approach (2nd Edition) by Russell and Norvig Chapter 13