CMSC 471

Artificial Intelligence -- Spring 2014

HOMEWORK FIVE
out 4/8/14; due 4/24/14

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

where arguments x have the domain of all people, and arguments t have the domain of all tests.
  1. Everyone who is smart, studies, and attends class will be prepared.
  2. Everyone who is prepared will pass a test if it is fair.
  3.  A student passes a test if and only if they don't fail it.
  4.  Every UMBC student is smart.
  5.  If a test isn't fair, everyone will fail the test.
  6.  Aidan is a UMBC student.
  7.  Sandy passed the 471 exam.
  8.  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.