Artificial Intelligence -- Fall 2011
NOTE: The material covered on this homework
assignment will be on the midterm on October 27. I have
kept the due date for the homework as November 1, but you
are strongly urged to complete the homework assignment
as part of your preparation for the midterm (even if you don't
neatly type it for submission). You can expect to see very
similar problems on the midterm, so completing this assignment
is one of the best ways that you can study for the midterm.
out Tues 10/18/11; due Tues 11/1/11
You are encouraged to work on this homework assignment in groups
of up to three students. If you work in a group, you only need to turn in one shared
solution. All students in the group will receive the same grade on the
assignment. If you choose to work in a group, you must actually
produce group solutions, not have each member
work independently on one part of the assignment, then submit the
collection of independent solutions. To acknowledge that you have
worked as intended, you must include the
following statement at the top of the submitted assignment:
"We, <students' names>, worked equally as a group
on this assignment, and each of us fully understands and acknowledges
the group solutions that we are submitting. We understand that we will
receive a common grade for this assignment."
Please be sure to include all group members' names on the assignment!
(Adapted from Russell & Norvig 2nd edition, Exercise 7.1.)
Describe the Wumpus world according to the properties of
task environments listed in Chapter 2 (i.e., the seven
characteristics described in Section 2.3.2). Your answer
should include a brief (single sentence or phrase)
justification for each of the seven answers..
Note: Use the
description of the Wumpus world from the book (not the online variations
that we saw in class).
I. Knowledge-Based Agents (15 points)
How would your answer change for a Wumpus variant in which the
wumpus could move according to fixed rules (i.e., rules
that are known to the agent)? How would your answer change
for a world in which the wumpus moved using an unknown
(a) Russell & Norvig Exercise 7.7, page 281 (15 pts).
II. Logic (55 points)
(b) Russell & Norvig Exercise 7.8 (b,c), page 281 (15 pts).
(c) Russell & Norvig Exercise 7.22 (a), page 284 (10 pts).
(d) Russell & Norvig Exercise 8.28 (c,f,h,k.l), page 321 (15 pts).
III. Resolution Theorem Proving (30 points)
(a) (8 points) Represent the following knowledge base in first-order logic.
Use the predicates
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.
(c) (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.