CS4811: Homework 2 --- Resolution


Due: Monday, January 30, 2006, beginning of class.
(Assigned: Monday, January 23, 2006.)

Reminder: This is an individual assignment. All the work should be the author's and in accordance with the university's academic integrity policies. You are allowed to use any source in preparing your answers, but if you use any other source than the current textbook and the current class notes, you should clearly specify it on your assignment.

Consider the following statements:

  1. If a resort has rental snowmobiles some people visiting there are happy.
  2. If a resort has no chalet nobody visiting there is happy.
  3. If a resort has no chalet, it has no rental snowmobiles.

Part A. Represent the above three statements in predicate logic using
S(X) for "resort X rents snowmobiles"
C(X) for "resort X has a chalet"
H(P) for "person P is happy"
V(P,X) for "person P visits resort X"

Part B. Set up the sentences so that the third can be proven using the first two employing resolution refutation. Then convert the sentences to clause form using the following steps:

  1. Eliminate → (implication)
  2. Reduce the scope of negation
  3. Standardize variables apart
  4. Move all quantifiers to the left without changing their order
  5. Eliminate existential quantifiers (Skolemize)
  6. Drop all universal quantifiers
  7. Convert expressions into conjunct of disjuncts form
  8. Make each conjunct a separate clause
  9. Standardize the variables apart again

Part C. Prove the third statement using resolution refutation.