# CMSC 471

### HOMEWORK FOUR

Due 10/29/07

Don't forget to include your statement of sources!

###

### I. Knowledge-Based Agents (15 points)

**Russell & Norvig Exercise 7.1.*** **Note:* Use the
description of the Wumpus world from the book (not the online variations
that we saw in class).

###

### II. Logic (55 points)

(a) **Russell & Norvig Exercise 7.5. (15 pts)**

(b) **Russell & Norvig Exercise 7.11 (a).** **(10 pts)**

(c) **Russell & Norvig Exercise 8.6 (a,b,c,i,j). (15 pts)**

(d) **Russell & Norvig Exercise 8.16.** **(15 pts)**

### III. Resolution Theorem Proving (30 points)

(a) (8 points) Represent the following knowledge base in first-order logic.
Use the predicates

`attend(x)`
` fail(x,t)`
` fair(t)`
` pass(x,t)`
` prepared(x)`
` smart(x)`
` study(x)`
` umbc-student(x)`

where arguments `x` have the domain of all people, and arguments `t`
have the domain of all tests.

- Everyone who is smart, studies, and attends class will be prepared.
- Everyone who is prepared will pass a test if it is fair.
- A student passes a test if and only if they don't fail it.
- Every UMBC student is smart.
- If a test isn't fair, everyone will fail the test.
- Aidan is a UMBC student.
- Sandy passed the 471 exam.
- Aidan attends class.

(b) (8 points) Convert the KB to conjunctive normal form.

(c) (2 points) We wish to prove that

`study(Aidan) -> pass(Aidan, 471-exam)`

Express the negation of this goal in conjunctive normal form.

(d) (12 points) Add the negated goal to the KB, and use resolution refutation
to prove that it is true. You may show your proof as a series of sentences
to be added to the KB or as a proof tree. In either case, you must
clearly show which sentences are resolved to produce each new sentence, and
what the unifier is for each resolution step.