1. [15 marks] Consider the following set of known facts and rules for a producti
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Question
1. [15 marks] Consider the following set of known facts and rules for a production system. (Check the Forward and Backward Chaining slides in the Rule Based Systems file in Module 3 for an example). Facts (known to be true): A, B, C Rules: 1. A ? D (means that if A is true then D is true) 2. B & C ? F (means that if B and C are both true then F is true) 3. C ? G 4. E & F ? H 5. G ? J 6. E ? L 7. I & L ? Z 8. H & J ? K 9. D ? I 10. B & D ? E 11. G & M ? N
[5 marks] Using backward chaining, prove that Z is true. Which rules would fire to accomplish this? What facts do we know after backward chaining has completed? c. [5 marks] Using this example, what have we learned about the applications for forward and backward chaining? Give an example of a situation where each would be the best choice.
Explanation / Answer
Answer:
Backward Chaining: It is a goal-driven strategy in which we hypothesize for a goal to be true and try find out which facts and rules from the existing rules and facts in the knowledge base will be applicable to reach the goal.
For the given condition, following facts are given:
Facts: A, B, C
that are known to be true.
And following are given:
1. A ? D
2. B & C ? F
3. C ? G
4. E & F ? H
5. G ? J
6. E ? L
7. I & L ? Z
8. H & J ? K
9. D ? I
10. B & D ? E
11. G & M ? N
Problem: We need to prove that Z is true. For as per backward chaining method, this is our goal.
Solution:
1. For Z to be true, rule 7 needs to be fired. For this rule to fire, I and L both should be true.
2. For I to be true, rule 9 needs to be fired. And for this rule to fire, D should be true.
3. For L to be true, rule 6 needs to be fired. And for this rule to fire, E should be true.
4. From rule 1, we can deduce that D is true since A being a fact is known to be true.
5. Based on inference of (4), we can conclude that I will also be true since D can be proved to be true.
6. Now having deduced that I is true, we need to conclude from (3) that E is true. From rule 10, we infer that E will be true provided B and D both are true. B being a fact is known to be true. And from (4), we have already inferred that D is true. So based on this, we can deduce that E will also be true.
7. Hence, from inference of 6, we can conclude L is true.
8. Now when we have deduced that both I and L can be concluded to be true from existing facts and rules, we can say that Z is also proved to be true.
Comparison of Forward Chaining and Backward Chaining: Forward chaining is data-driven strategy, while Backward chaining is goal driven strategy. Forward chaining is appropriate in situations that needs to answer "what can happer next?". While Backward chaining is appropriate for the situations that needs to answer "Why this happened?". Forward chaining is normally applied when a set of facts is available, but conclusion is not known. On the other hand, Backward chaining can be considered when few or one possible conslusions are available alongwith many possible facts not directly applicable to conclusions.
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