### CSCI 3202: Artificial Intelligence, Fall 2000

#### Problem Set 3

Handed out: Monday, Oct. 23
Due back: Monday, Nov. 6

#### Problem 1. (45 points) A Rule-Based System

Shown here are fifteen rules for a rule-based system named "Zookeeper" (from Winston's text Artificial Intelligence). The system's job is to identify animals in a small zoo. All the rules shown are of the form "IF condition1 AND condition2 AND ... THEN consequent".

1.1 (15 points)
Assume that we know the following facts (and nothing else) about an animal, Splashy:

Splashy has feathers.
Splashy lays eggs.
Splashy does not fly.
Splashy is black and white.

Now assume that the Zookeeper system is asked to perform backward chaining from the following hypotheses in the given order:

Ostrich
Penguin
Albatross

Simulate Zookeeper's behavior so as to determine what kind of animal Splashy is, using the hypotheses in the specified order. Indicate your answer by showing what is the sequence in which the rules are used, what each rule is trying to do, and whether each rule succeeds.

1.2 (15 points)

Now assume that we add a couple of additional facts (without removing any of the previous facts, which remain unchanged):

Splashy has long legs.
Splashy has a long neck.

Suppose the Zookeeper rule system is asked to perform forward chaining starting from its augmented set of seven facts (and nothing else). Why is the result peculiar? What sort of programming strategy would be needed to fix the problem?

1.3 (15 points)

Add rules to the Zookeeper system so that it can recognize raccoons, elephants, rhinos, and buffalo. Make each rule just strong enough to separate the recognized animal from the (small number of) others in the zoo, rather than from all possible animals. (Zoological note: elephants, rhinos, and buffalo are all ungulates; elephants and rhinos are both pachyderms, or thick-skinned non-cud-chewing ungulates.)

#### Problem 2. (55 points) Bayesian Probability

Consider the following belief network concerning the Rockies:

The meaning of the nodes is as follows:

H: Helton plays today.
W: (Larry) Walker plays today.
R: Rockies lose today.
B: Buddy Bell grumpy this evening.
M: Mike grumpy this evening.
D: Mike's dog Rhombi grumpy this evening.

The basic probabilities in the network are as follows:

P(H) = 0.8
P(W) = 0.2
P(R | HW) = 0.25
P(R | H notW) = 0.5
P(R | notH W) = 0.5
P(R | notH notW) = 0.75
P(B | R) = 0.8
P(B | not R) = 0.4
P(M | R) = 0.6
P(M | not R) = 0.3
P(D | M) = 0.4
P(D | not M) = 0.01

2.1 (15 points)

Calculate each of the following probabilities:

P(R): probability that the Rockies lose on a given day.
P(B): probability that Buddy Bell is grumpy on a given day.
P(M): probability that Mike is grumpy on a given day.
P(D): probability that Rhombi is grumpy on a given day.
P(B and M): probability that both Buddy Bell and Mike are grumpy on a given day.

2.2 (20 points)

Calculate each of the following probabilities:

P(D|R): probability that Rhombi is grumpy given that the Rockies lost
P(B and D|notR): probability that both Buddy Bell and Rhombi are grumpy given that the Rockies won
P(H| R): probability that Helton played given that the Rockies lost.
P(H|M): probability that Helton played given that Mike is grumpy.

2.3 (20 points)

Calculate the following probabilities:

P(notH and notW| B and M): probability that neither Helton nor Walker played given that both Buddy and Mike are grumpy.

P(W|D): probability that Walker played given that Rhombi is grumpy.