## Problem Set 2

Assigned: Feb. 12

Due: Mar. 5. NOTE EXTENDED DUE DATE

### Problem 1

What is the result of doing alpha-beta pruning in the game tree shown
below?

### Problem 2

Use propositional resolution to prove (a) from (b-e).
- a. (not p) < = > (q ^ r)
- b. p V q.
- c. p V w.
- d. w => r.
- e. p => (not (q ^ r))

### Problem 3

Let *L* be a first-order languge where the entities are people
and places. *L* contains the following non-logical symbols:
a(X) -- X is an adult.

b(X) -- X is a baby.

c(X,Y) -- X is taking care of Y.

p(X,L) -- X is at place L.

j,k -- Constants. Joe and Karen.

g -- Constant. The playground.

Express the following sentences in *L*:
- 1. If B is a baby, then there exists an A who is taking care of B.
- 2. If A is taking care of B, then for any place L, A is at L if and
only if B is at L.
- 3. If A is taking care of B, then A is an adult and B is a baby.
- 4. If A is in the playground and A is an adult, then there exists a baby
B such that A is taking care of B. (That is, adults are only allowed in
the playground if they are taking care of a baby.)
- 5. Everyone who is taking care of Joe is also taking care of Karen.
- 6. Joe and Karen are babies.
- 7. If there are no babies in the playground, then there are no
adults in the playground.
- 8. For every place L, if Joe is at L then Karen is at L.

### Problem 4 IS REINSTATED, DUE TO POSTPONEMENT OF DUE DATE.
Construct resolution proofs of (7) and of (8) from (1-6) in problem 3.
You should show (a) the Skolemized form of each axiom and each
negated goal; (b) every resolution done in the proof. You need not
show the intermediate stages of Skolemization.