Rule-based systems exercise answer sheet Page 1 6.871 Problem Set 2 RULE-BASED SYSTEMS EXERCISES ANSWER SHEET Exercise 1: SIMULATING THE INFERENCE ENGINE A) Run the system by hand, following the procedure outlined above. Show what happens by drawing the tree of rules, by augmenting Worksheet 1 and indicating the dialog that would occur and the additions to the database by augmenting Worksheet 2 Use the following data: 1. The user is 42 years old 2. has health and life insurance 3. has current savings balance of $20000 4. has a monthly salary of $3000 5. not covered by a pension plan, does have IRA 6. has one child, age 12, who does not have scholarship or a trust fund, is not eligible for a loan, and would like to attend a school with expensive tuition 7. does not currently own a house and would like to.Rule-based systems exercise answer sheet Page 2 WORKSHEET 1 category insurance coverage health ins life ins should have 10 2 1Rule-based systems exercise answer sheet Page 3 WORKSHEET 2 DIALOG DATABASE Attribute Value Source 1) Do you have health insurance? ** YES HaveHealthInsurance Yes user, quest. 1Rule-based systems exercise answer sheet Page 4Rule-based systems exercise answer sheet Page 5 B) How would the program respond if, in answer to the question “do you have an pension”, you had answered “WHY”? (Hint: recall the mechanism used for explanation) Do you have a pension? ** WHY C) How would the program respond to the question shown below? (Hint: recall that the system displays the “audit trail” of the rules used to reach that conclusion, i.e., all the rules that lead to that specific answer.) HOW DID YOU DECIDE THAT THE INVESTMENT SHOULD BE CONSERVATIVE GROWTH? D) How would the program respond to the question HOW DID YOU DECIDE THAT THE INVESTMENT SHOULD BE GROWTH AND INCOME?Rule-based systems exercise answer sheet Page 6 Exercise 2: DEALING WITH UNCERTAIN RULES A) Using the scheme outlined above, what would be the resulting degree of belief from the following sequence of rules (assume all are relevant, and note that some certainties are negative): I) If ... then investment should be G&I .6 II) If ... then investment should be G&I –.2 III) If ... then investment should be G&I .8 IV) If ... then investment should be G&I –.45 (B) What happens if the rules fire in the order (IV) (II), (III), (I)? Does this seem intuitively reasonable? Why, or why not? C) What would the strength of conclusion be if the user had answered .9?Rule-based systems exercise answer sheet Page 7 D) Work through the certainties that would be computed by the three rules below. (Note that this example exercises all of the machinery we need for certainties. We have abbreviated the premises and conclusions to single letters, to simplify things and focus on the issue of modeling uncertainty.) (I) If A and B then E .7 (II) If C or D then not E .45 (i.e., E with a certainty of -.45) (III) If E then X .8 Assume that the user answers the questions as follows: A? ** YES .8 B? ** YES .9 C? ** YES .9 D? ** YES .5 How strongly do we now believe X? E) Work through the certainties that result from the following four rules, assuming that the user's answers to F, G, H, J, and K are all YES with certainty 1.0. (I) If F then Y .7 (II) If G then Y .8 (III) If H then Y .5 (IV) If J then Y .6 What is the strength of belief in Y at this point?Rule-based systems exercise answer sheet Page 8 Imagine that we had the two additional rules (V) and (VI) shown below and that they fired. Would we be absolutely certain in our belief in Y? (V) If J1 then Y .7 (VI) If J2 then Y .8 Now imagine that rule (VII) fires. Now how strong is our belief in Y? (VII) If K then Y 1.0 What does this demonstrate about the strength of belief accumulating function?Rule-based systems exercise answer sheet Page 9 Exercise 3: RULES ARE SUPPOSED TO CAPTURE THE LOGIC OF THE SITUATION A) As in Exercise 1, show the dialog would result from traversing this tree and the additions to the database that would result. Use the degree of certainty machinery we just reviewed. Note that you have far less work to do on this problem because we have given you the entire tree. You only have to traverse it, and show the dialog and conclusions. The user 1. is 70 years old 2. does not have health insurance 3. does have life insurance 4. has a current savings balance of $20000 5. has a monthly salary of $3000 6. is covered by a pension plan 7. has no children 8. currently owns a home What is the system's recommendation?Rule-based systems exercise answer sheet Page 10 Category Basic Insurance INADEQUATE Savings > 6 * Salary Goal = RETIRE Goal = RETIRE Goal = RETIRE Ytr<10 10<ytr<20 Ytr<10 Oldest<7 Goal = EDUCATIONGoal = EDUCATIONOldest>7 Goal = HOME Goal = INCOME Goal = INVEST Goal = INVEST Goal = INVEST Goal = INVEST Risk = LOW Risk = MEDIUM Risk = HIGH Risk = LOW Health = NO Should = YES Life = NO Health = YES Pension = NO Life = YES Ira = NO Headed = YES Funded = NO Bracket = HIGH Own = NO Want = Yes LifeStage= RETIRED Own = YES Pension = YES Children = NO LifeStage = NOT-RETIRED Age > 65 Age < 65 Want = NO Ira = YES Funded = YES Children = YES Children = YES Children = NOYoungest < 16 Youngest >= 16 10 11 12 13 14 15 16 17 18 19 20 21 22 1 2 3 31 32 34 35 45 46 47 23 24Rule-based systems exercise answer sheet Page 11 WORKSHEET 3 DIALOG DATABASE Attribute Value SourceRule-based systems exercise answer sheet Page 12Rule-based systems exercise answer sheet Page 13 B) Now suppose rule 10 were moved down the page to the end of the list of rules concluding about fund category (i.e., after rule 22). Describe what difference this makes in the trace of the reasoning process and in the dialog. Also, does this change the final result? (As in earlier exercises, this should not require a great deal of work if you think carefully and rely on what you did in the previous part of this exercise.)Rule-based systems exercise answer sheet Page 14 Exercise 4: KNOWLEDGE ACQUISITION A) Try writing two rules to help out. Do this by filling in the blanks below. Use anything you know that is a good plausible guess. Remember that we're trying to come up with good guesses