Category6.871 Problem Set 2RULE-BASED SYSTEMS EXERCISES ANSWER SHEETThe user6.871 Problem Set 2RULE-BASED SYSTEMS EXERCISES ANSWER SHEETExercise 1: SIMULATING THE INFERENCE ENGINEA) Run the system by hand, following the procedure outlined above. Show what happensby drawing the tree of rules, by augmenting Worksheet 1 and indicating the dialog thatwould occur and the additions to the database by augmenting Worksheet 2Use the following data:1. The user is 42 years old2. has health and life insurance3. has current savings balance of $200004. has a monthly salary of $30005. not covered by a pension plan, does have IRA6. 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 tuition7. does not currently own a house and would like to.Rule-based systems exercise answer sheet Page 1WORKSHEET 1 Rule-based systems exercise answer sheet Page 2category insurance coveragehealth ins life ins should have1021WORKSHEET 2DIALOG DATABASEAttribute Value Source1) Do you have health insurance?** YES HaveHealthInsurance Yes user, quest. 1Rule-based systems exercise answer sheet Page 3Rule-based systems exercise answer sheet Page 4B) 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?** WHYC) 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 thatconclusion, 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 questionHOW DID YOU DECIDE THAT THE INVESTMENT SHOULD BE GROWTH AND INCOME?Rule-based systems exercise answer sheet Page 5Exercise 2: DEALING WITH UNCERTAIN RULESA) Using the scheme outlined above, what would be the resulting degree of belief from thefollowing sequence of rules (assume all are relevant, and note that some certainties arenegative):I) If ... then investment should be G&I .6II) I f ... then investment should be G&I –.2III) If ... then investment should be G&I .8IV) If ... then investment should be G&I –.45(B) What happens if the rules fire in the order (IV) (II), (III), (I)? Does this seemintuitively 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 6D) 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 haveabbreviated the premises and conclusions to single letters, to simplify things and focus onthe 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 .8Assume that the user answers the questions as follows:A?** YES .8B?** YES .9C?** YES .9D?** YES .5How strongly do we now believe X?E) Work through the certainties that result from the following four rules, assuming that theuser'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 .6What is the strength of belief in Y at this point?Imagine that we had the two additional rules (V) and (VI) shown below and that theyfired. Would we be absolutely certain in our belief in Y?Rule-based systems exercise answer sheet Page 7(V) If J1 then Y .7(VI) If J2 then Y .8Now imagine that rule (VII) fires. Now how strong is our belief in Y?(VII) If K then Y 1.0What does this demonstrate about the strength of belief accumulating function?Rule-based systems exercise answer sheet Page 8Exercise 3: RULES ARE SUPPOSED TO CAPTURE THE LOGIC OF THE SITUATIONA) As in Exercise 1, show the dialog would result from traversing this tree and theadditions to the database that would result. Use the degree of certainty machinery we justreviewed. Note that you have far less work to do on this problem because we have given you theentire tree. You only have to traverse it, and show the dialog and conclusions.The user1. is 70 years old2. does not have health insurance3. does have life insurance4. has a current savings balance of $200005. has a monthly salary of $30006. is covered by a pension plan7. has no children8. currently owns a homeWhat is the system's recommendation?Rule-based systems exercise answer sheet Page 9Rule-based systems exercise answer sheet Page 10CategoryBasic InsuranceINADEQUATESavings >6 * SalaryGoal =RETIREGoal =RETIREGoal =RETIREYtr<10 10<ytr<20 Ytr<10Oldest<7Goal =EDUCATIONGoal =EDUCATIONOldest>7Goal =HOMEGoal =INCOMEGoal =INVESTGoal =INVESTGoal =INVESTGoal =INVESTRisk = LOW Risk =MEDIUMRisk = HIGHRisk = LOWHealth = NOShould = YESLife = NO Health =YESPension = NOLife = YES Ira = NOHeaded =YESFunded = NOBracket =HIGHOwn = NOWant = YesLifeStage=RETIREDOwn = YES Pension =YESChildren =NOLifeStage = NOT-RETIREDAge > 65 Age < 65Want = NO Ira = YES Funded = YESChildren = YES Children = YES Children = NOYoungest < 16 Youngest >= 161011 12 131415 1617 1819 2021 221 2 3 31 32 343545 464723 24WORKSHEET 3DIALOG DATABASEAttribute Value SourceRule-based systems exercise answer sheet Page 11Rule-based systems exercise answer sheet Page 12B) Now suppose rule 10 were moved down the page to the end of the list of rulesconcluding about fund category (i.e., after rule 22). Describe what difference this makes inthe 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 carefullyand rely on what you did in the previous part of this exercise.)Rule-based systems exercise answer sheet Page 13Exercise 4: KNOWLEDGE ACQUISITIONA) Try writing two rules to help out. Do this by filling in the blanks below. Use anythingyou know that is a good plausible guess. Remember that we're trying to come up withgood guesses here, not absolute, hard and fast answers.If ___________________ then the tuition is likely to be EXPENSIVE.If ___________________then the tuition is likely to be CHEAP.B) Why is it true that we need look at only this one part of the tree? We added rules 60and 61 to the knowledge base, and gave no further guidance, yet without re-running thewhole example we can say