Artificial intelligence required

Cl1/A4.docx

A4

Book: Artificial Intelligence A Modern Approach Second Edition.

Author: Stuart Russell and Peter Norvig

Please provide a quote to provide complete solution

Chapter: 8 and 9

1. The equality symbol of first-order logic is not always appropriate. Why is it valid to say Supervisor(John) = Henry but it is probably not valid to say Supervises(Henry) = John?

2. Consider the following attempts to create first-order logic statements. In each group, determine which statement best expresses the meaning of the English sentence, and explain why (explain the problems with the other choices).

3. Assume that sentences exist defining Brother, Mother, and Father. Create sentences in first order logic that represent the following:

a. If x is the mother or father of y, then x is y's parent.

b. If x is the uncle of y, then y's parent must have x as a brother (you can make use of the Parent sentence you defined in part a).

4. Represent the following sentences in first-order logic, using a consistent vocabulary that you define:

a. Bob shops at the mall.

b. Everyone who shops at the mall is wealthy.

c. No one lives at the mall.

5. Of the following, which is an example of universal instantiation, and which is an example of existential instantiation? Explain.

6. These refer to the inferences of the previous question.

a. Does the first inference prove that someone named Heinrich bakes pie? Explain.

b. Does the second inference prove that Belbo eats pie? Explain.

7. What is "standardizing apart" and why is it necessary for the unification process?

8. Suppose we have the following rules:

a. What do these translate to in English?

b. Unify the second rule with the following sentence in our knowledge base (standardize apart if necessary):

ThreatenedBy(x, Sun)

9. The following refer to forward chaining.

a. Describe the problem of irrelevant facts.

b. How can we use a "magic set" to eliminate this problem?

10. Over the next few questions, you will simulate the role of detective by solving the following logic problem via proof by resolution.

The maid said that she saw the butler in the living room. The living room is near the kitchen. A gunshot was fired in the kitchen. The butler, who has good hearing, said he did not hear the shot.

The following notation and function definitions are provided:

Told_truth(x): Person x told the truth

Was_in(x, y): Person x was in room y

Was_near(x, y): Person x was near room y

Heard_gunshot(x, y): Person x heard the gunshot in room y

For this question, provide the first order logic statements for each of the following. Include quantifiers as necessary.

a. If anyone, x, was in the living room, then that person, x, was near the kitchen.

b. If anyone, x, was near room y, then that person heard the gunshot in room y.

c. If the maid told the truth, then the butler was in the living room.

d. If the butler told the truth, then he did not hear the gunshot in the kitchen.

e. The maid told the truth.

11. Convert each of the first-order logic statements from the previous question into conjunctive normal form.

12. Use the CNF statements from the previous question to prove the butler is lying. To do this, assume the opposite: add Told_truth(Butler) to the knowledge base and generate new clauses until you reach the empty clause. Show each step in the process by making a simple table, showing the two clauses being combined and the result.