CSE 4308/5360 - Exams - Preparation for Second Midterm

Material

The material covered in this midterm consists of the following chapters and sections in the textbook:

Chapter 8, sections 8.1, 8.2, 8.3.
Chapter 9, sections 9.1, 9.2, 9.3, 9.4, 9.5.
Chapter 11, sections 11.1, 11.2, 11.3, 11.4, 11.5.
Chapter 12, sections 12.3, 12.4, 12.5.
Chapter 13, sections 13.1, 13.2, 13.3, 13.4, 13.5, 13.6.
Chapter 14, sections 14.1, 14.2, 14.3.

Practice Questions - Answers

What is the negation of each of the following sentences?
```
1. for-every x, exists y: son(x) = y
2. for-every x, for-every y: son(x) = y <=> father(y) = x
```
In your answers, any "not" may only appear after the last appearance of a universal or existential quantifier.
Textbook exercise 8.8.

Consider the technique of propositionalization. For each of the following two knowledge bases, decide if propositionalization can be applied successfully. If not, why not?

KB 1:

for-every x: king(x) and greedy(x) => evil(x)
king(John)
greedy(John)
brother(Richard, John)


KB 2:
for-every x: king(x) and greedy(x) => evil(x)
king(John)
greedy(John)
brother(Richard, John)
king(father(John))

What is the most general unifier for each of the following pairs of expressions:

1. major(John, x), major(y, mathematics)
2. major(John, x), major(y, z)
3. major(John, x), major(y, x)
4. major(John, x), major(x, y)

Textbook exercise 9.3, parts (a), (b)
Textbook exercise 9.4.
Textbook exercise 9.19, parts (a), (b), (c).
Textbook exercise 11.2.
Textbook exercise 11.8.
Textbook figure 11.4 provides a description for a deterministic version of the blocks world. We want to make a modification to that description, so as to model a nondeterministic version, in which the effect of action move(b, x, y) is sometimes on(b, y) and sometimes on(b, table). How would you modify the description of the move action to make it reflect the above two possible outcomes of move(b, x, y)?
In the nondeterministic blocks world described in the previous exercise, suppose that the initial state and the goal are as described in figure 11.4. Is there a finite conditional plan that achieves this goal with guaranteed success? If yes, list the sequence of actions in that plan. If no, explain why not.
1. Is the following function P a valid probability function? If you answer "no", explain why not.
```
P(day == Monday) = 0.4
P(day == Tuesday) = 0.4
P(day == Wednesday) = 0.2
```
2. Is the following function P a valid probability function? If you answer "no", explain why not.
```
P(day == Monday) = 0.4
P(day == Tuesday) = 0.4
P(day == Wednesday) = 0.2
P(day == Thursday) = 0.1
```
3. Is the following function P a valid probability density function? If you answer "no", explain why not.
```
P(x) = 0.1, if 10 <= x <= 20.
P(x) = 0 otherwise.
```
4. Is the following function P a valid probability density function? If you answer "no", explain why not.
```
P(x) = 0.01, if 10 <= x <= 20.
P(x) = 0 otherwise.
```

Compute P(fire | alarm), given the following information:

P(alarm | fire) = A
P(alarm | not fire) = B
P(fire) = C

We are given the following information:
```
P(fire) = 0.1
P(earthquake) = 0.2
P(flood) = 0.4
```
1. Suppose that we do not know whether fire, earthquake, and flood, are independent events. Can we compute the probability P(fire and earthquake and flood)? If yes, what is P(fire and earthquake and flood)?
2. Suppose that we know that fire, earthquake, and flood, are independent events. Can we compute the probability P(fire and earthquake and flood)? If yes, what is P(fire and earthquake and flood)?
3. Suppose that we know that fire, earthquake, and flood, are not independent events. Can we compute the probability P(fire and earthquake and flood)? If yes, what is P(fire and earthquake and flood)?

Compute P(commute time < 20 min | temperature > 80), given the following joint probability distribution:

Commute time  40-60 Fahrenheit 60-80 Fahrenheit   above 80 Fahrenheit
< 20 min      0.1              0.05               0.1 
20-40 min     0.2              0.1                0.1
> 40 min      0.05             0.1                0.2

For the Bayesian network shown in textbook figure 14.2: is P(Earthquake | Alarm) larger, equal to, or smaller than P(Earthquake | Alarm and Burglary)? You can either (not recommended) compute both probabilities, or (recommended) provide an intuitive (but correct) justification for your answer.
For the Bayesian network shown in textbook figure 14.2: is P(Earthquake | Alarm) larger, equal to, or smaller than P(Earthquake | Alarm and MaryCalls)? You can either (not recommended) compute both probabilities, or (recommended) provide an intuitive (but correct) justification for your answer.