Longer example of backward chaining

Start with this knowledge base. A simple set of rules to infer which resort a skier should go to, given his purpose (to have fun or to practise serious skiing), the number of lessons he's had so far, and the number of press-ups he can do without collapsing. Scenario: this knowledge base is built into an expert system. A client comes along for a consultation.

1 Resort = st sartre if
      Rating = beginner and
      Purpose = fun.

2 Resort = schloss heidegger if
      Rating = beginner and
      Purpose = serious.

3 Resort = chateau derrida if
      Rating = advanced and
      Purpose = serious.

4 Resort = wittgenstein gladbach if
      Rating = advanced and
      Purpose = fun.

5 Rating = beginner if
      Lessons < 30.

6 Rating = beginner if
      Lessons >= 30 and
      Fitness = poor.

7 Rating = advanced if
      Lessons >= 30 and
      Fitness = good.

8 Fitness = poor if
      Pressups < 10.

9 Fitness = good if
      Pressups >= 10.

In an expert system, we have to distinguish between observable or askable data which the client can supply, and computable data which the system calculates using the rules. Let's suppose that Pressups, Fitness, Purpose are askable. A real expert system language would make you specify that with the rules. Suppose also that the goal is to find a value for Resort.

So: goal is to find Resort. Do we know it already? No. So start by locating all rules which can tell you about Resort, i.e. which have it in their conclusions. These are rules 1, 2, 3, and 4.

Now, we have to investigate one or more of these rules. There are many possible orders: serially from top to bottom; serially from bottom to top; in parallel; etc. For simplicity, assume serial top to bottom. So we start with rule 1.

Test its conditions next. Do we know a value for Rating? No. Is Rating askable? No. So we have to calculate it from another rule; we can't ask the client for it.

So we now set a subgoal of calculating Rating. Locate all rules which have it in their conclusions. These are 5, 6, 7. Start with rule 5.

Test its conditions next. Do we have a value for Lessons? No. Is Lessons askable? Yes. So we ask the client for it. He types in 178. We store this in STM. Now, is Lessons less than 30? No. So the condition fails. Rule 5 can't tell us anything, so we go on to rule 6.

Test its conditions next. Do we have a value for Lessons? Yes, we do now. Is Lessons 30 or more? Yes. So the first part of the condition succeeds. Go on to Fitness. Do we have a value for Fitness? No. Is it askable? No. So we have to calculate it.

So we now set another subgoal of calculating Fitness. Locate all rules which have it in their conclusions. These are 8 and 9. Start with 8.

Test its conditions. Have we a value for Pressups? No. Is it askable? Yes. Ask the client. He types 15. Store it in STM. The condition fails, so abandon rule 8 and go on to 9. That condition succeeds, so we conclude Fitness = good. Store that in STM.

Now we've finished with the latest subgoal, so we return up a level, to rule 6. Its condition fails. So we go on to rule 7. Its condition succeeds. So we have now achieved the subgoal of calculating Rating. We can back up another level, to rule 1. Its conditions fail. Go on to rule 2, which also fails. Go on to rule 3. The first part of its condition succeeds; what about the second? Do we know Purpose? No. Is it askable? Yes. Ask the client. He types fun. So the condition fails. Go on to rule 4. This one's conditions succeed, we now have a value for Resort, and everyone's happy, especially me because I know I can always get a job as an expert system if all else fails.