Final Exam Sample Questions (revised 12/11/01)

The final exam will be cumulative.

The materials of the programming assignments are testable.

Also see the sample questions from Midterm 1 and Midterm 2.

The contents of Reading 1, and Reading 2 are testable.

The contents of Exercise 1, and Exercise 2, are possible question types as well.

Chapter 6: Agents that Reason Logically (Continued)

6.1. Define the following terms: Monotonicity, Horn sentence

6.2. Give a reason why propositional logic is not suitable for a full solution of the wumpus world problem.

6.2. Write (define) a Scheme function named ConvertImplication that takes one parameter: a list of the form: (implies P Q). The function should remove the "implies" and instead returns a Scheme format logical sentence containing a disjunction and a negation: i.e., (or (not P) Q).

6.3. Write (define) a Scheme function named MoveNegation that takes one parameter: a list of the form (not (-OP- R S)) where -OP- can be "and" or "or". This function changes the expression, moving the negation closer R and S, and returns that resulting formula. For example, if the input is (not (and R S)), then the result of the function should be (or (not R) (not S)). If the input is (not (or R S)), then the result should be (and (not R) (not S)).

Chapter 7 & 9: First-Order Logic & Inference in First Order Logic

7.1. Solve the following unification problems by providing a most general unifier, or explaining why the pair of formulas cannot resolve:

(a) (P ?y), (Q ?y)

(b) (P ?y ?y), (P ?r ?x)

(c) (M (G ?x)), (M ?y)

(d) (P A), (P ?x)

(e) (P A), (P B)

7.2. Using the rules from the set theory domain (see p. 199-200 in text), prove that the element B is not in the set Adjoin(C, Adjoin(A, EmptySet)).

7.3. Using the rules from the set theory domain (see p. 199-200 in text), prove that the element B is in the set Union(Adjoin(A, EmptySet), Adjoin(B, EmptySet)).

7.4. Define the following terms: Frame axiom, effect axiom, successor-state axiom.

7.5. Define Unification in terms of Substitution.

7.6. Unify (p, q) = theta. What is theta? Give an example.

7.7. Resolution inference normally proceeds as proof by contradiction. What is proof by contradiction? When does an algorithm using proof by contradiction end or terminate? Give an example of a last step of a proof by contradiction proof. What can you infer when the proof ends?

7.8. What is Conjunctive Normal Form (CNF)? What does a knowledge-base look like that has been converted to CNF? Give a brief, but sufficient example. Explain the notational assumptions in the CNF example KB you give.

7.9. Skolemize the following first-order logic sentence: (ThereExists x (Apple(x)))

7.9. Skolemize the following first-order logic sentence: (Forall f (ThereExists c (Father(f, c)))

7.9. Given the following formulas to be converted to CNF and placed into a KB (~ is the negation symbol):

(Forall x (P(x) => Q(x)))

(Forall x (~P(x) => R(x)))

(Forall x (Q(x) => S(x)))

(Forall x (R(x) => S(x)))

(a) convert the formulas to CNF

(b) prove S(x) by resolution refutation (resolution using contradiction).

Chapter 10: Logical Reasoning Systems (Covered by T. Colburn)

10.1. Define: production system, frame system, semantic network

10.2. How does Prolog relate to Horn clauses?

Chapter 14: Uncertainty

14.1. Define: Prior probability, mutual exclusive events, independent events

14.2. Mathematically express definitions for: conditional probability, Bayes rule, product rule

14.3. Given that you have been given real number values for: P(A | B), P(~A | B), P(A | ~B), P(~A | ~B), show the algebra to calculate P(B | A).

Chapter 15: Probabalistic Reasoning Systems

15.1. Define: Causal reasoning, diagnostic reasoning

15.2. In computer vision systems, there can be influences both from sensors and models of the world (e.g., "expectation"). Consider the following events with a computer vision system that is detecting the presence or absence of an object.. Let O be the (boolean) event that an object is present. Let E be the (boolean) event that we are expecting an object to be present. Let S be the (boolean) event that our camera sensor indicates the object is present. Let Sf be the (boolean) event that our camera sensor is faulty. Let D be the (boolean) event that the vision system detects the object. The presence of an object (O) influences the vision sensor (S). The system's "expectation" (model) influences whether the system detects the object (D).

(a) Draw the Bayesian belief network corresponding to this situation.

(b) Given the following prior and conditional probabilities, compute the causal probability that we detect an object given that the camera is not faulty and we expect an object.

P(Sf) = 0.01; P(O) = 0.7; P(E) = 0.5

(c) Interpret your result. i.e., explain what the probablity you have computed means.

15.3. Sensors in robotic or biological systems generally have noise. That is, there will be some error associated with the information obtained from the sensors. Logical systems such as resolution theorem provers assume a complete and consistent set of wffs in their KB's. There is an apparent conflict between these two issues. On the one hand, sensors have noise. On the other hand, logical systems require complete and consistent formulas. Suppose you are designing an AI system that operates in the real world (e.g., a robotic system):

(a) State and describe two problems that would likely arise from this apparent conflict.

(b) Suggest ways that we might use to get around these problems.

Chapter 18: Learning From Observations

18.1. Define the following terms: supervised learning, unsupervised learning, online learning, offline learning, dimension space reduction, generalization, bias

18.2. Suppose you are representing a feature, S (size) with attribute values: huge, large, medium, small, tiny.

(a) With no other assumptions, how many bits of information will it take for you to represent a single item's category?

(b) Say that we know some frequency information about the size category. Suppose P(S=huge) = .2, P(S=large) = .3, P(S= medium) = .4, P(S =small) = .04, P(S=tiny)= 0.06. Calculate the average information required to represent an item's category, given this frequency information, and given that we are representing many items.

18.3. (a) Generate a minimal height decision tree for the following examples. The question being asked is: Should tennis be played? Use the information theory approach to compute the next feature(s) to be included in the decision tree.

(b) Express in English the rule formed by the decision tree.

(Example due to T. M. Mitchell)