CMSC 471
Artificial Intelligence -- Fall 2014
HOMEWORK FOUR
out 11/13/14; due 12/3/14
I. Knowledge-Based Agents (15 points)
(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.
How would your answer change in a world 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
mechanism?
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 7.7, page 281 (15 pts).
(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 320-321 (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.
(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.