CS 4804 Homework #7

1. (30 points) An AI system is used to estimate whether or not people are good credit risks based on a number of factors that combine to produce a numeric score. To be judged a good credit risk, the score must be higher than some number N. The designers of the system won't say what the value of N is, but we have learned that Pete is judged to be a good credit risk and that Joe's score is higher than Pete's.
   
   It is obvious that we can prove that Joe would be judged to be a good credit risk too. (10 points) Show how we can prove this by stating the given facts and axioms in predicate logic and performing resolution-refutation. (10 points) Then draw the proof tree with the root as the conclusion "Joe is a good credit risk" and the leaves as the given facts. (10 points) Draw a cutting plane through the tree and create a general rule for use in later situations (i.e., you are performing explanation-based learning).
   
   
2. (30 points) An AI learning agent observes that everytime Q is true, one of the following formulas is also true:

   
   P(A,B).
   P(C,B).
   P(D,B).
   

   Based on this observation, the agent decides to create the rule:
   
   forall x, P(x,B)->Q
   
   What type of learning is the agent performing: (i) explanation-based learning, (ii) relevance-based learning (type 2 learning), or (iii) inductive logic programming? Give reasons. Why do you think the agent did not create the following rule?
   
   forall x,y P(x,y)->Q
   
   
3. (40 points) Assume that we apply resolution to two clauses C1 and C2, to get the resolvent C. C is given to be the formula "R(B,x) disjunction P(x,A)". C1 is given to be the formula "S(B,y) disjunction R(z,x)." Apply inverse resolution and give at least four possible values for C2.