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# Backward Chaining

Posted on 2010-11-11
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Could you explain backward chaining? For example how would I handle

1 - allergies(x) => sneeze(x)

2 - cat(y) ^ allergic-to-cat(x) => allergies

3 - cat(Felix)

4 - allergic-to-cat(Lisa)

Goal: Sneeze(Lisa)
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Question by:JCW2
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LVL 37

Expert Comment

ID: 34117957
You start from the back. So in order to get Sneeze(Lisa) you select a rule that could lead you there and add it to the list of goals. In this case the only rule that does this is rule 1. So now the list of goals is just allergies(Lisa)=>Sneeze(Lisa) (replacing x with Lisa). So this is your new goal (in more complicated questions you may have multiple goals in the list at a time).

So what could get you to the new goal? Pick all the rules that could get you there and make those the goals (in this problem you'll only have one again)

If you run into a problem where you have more than one goal at some point, just do the same thing for all the goals.

What I would do is just write the goal and then draw an arrow to all the new goals and write them.
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LVL 37

Expert Comment

ID: 34117967
And you just keep going until you get a goal that is given directly by a rule or by the given conditions of the problem.
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Author Comment

ID: 34123022
Can you describe how to work with this:
BC.PNG
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LVL 37

Expert Comment

ID: 34123088
Yes. It's saying to do the same thing I said.

q = Goal

"check if q is known already"
Do you have a rule or a given statement that says q is true?

"prove by BC all premises of some rule concluding q"
Take all the rules that have q on the right hand side and add them to the goal list.
Do the last two steps for each of them.
Note that this will continue until you find a rule that directly says one of your goals is true.

"Avoid loops"

"Avoid repeated work"
If you add a goal to the list but you already proved it true or false, don't add it. Just use true or false.
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Author Comment

ID: 34125850
I need to demonstrate use of a stack when implementing backward chaining. How should I do this?
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LVL 37

Expert Comment

ID: 34125936
By each step of the process put your entire goal list (stack). So in the first step, the stack will have one goal. In the second step, two goals, etc. Of course if two rules will satisfy a goal you'll add two new goals to the stack at once.
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Author Comment

ID: 34129051
Would the stack look anything like this:
Stack.PNG
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LVL 37

Accepted Solution

TommySzalapski earned 500 total points
ID: 34129266
Absolutely. The only thing I'd do differently is mark the 'active' goals (the ones that have not been satisfied by other goals).
So in steps 1 and 2, I'd put a mark by the top goal and in step 3 the top 2 goals.
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Author Closing Comment

ID: 34146910
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