AI: Problem Set 4

Assigned: March 4
Due: March 25

Problem 1

Let D be a domain containing solid objects. Let L be the first-order language over D with the following non-logical symbols:
i(O1,O2) --- Object O1 is inside O2.
h(O) --- O is hollow.
r(O) --- O is red.
s(O) --- O is small.
m(O) --- O is medium-sized.
b(O) --- O is big.
ox --- Constant symbol.

A. Represent the following statements as Horn clauses in L.

B. Prove the statement ``There exists a hollow red object'' using backward chaining.

C. Prove the statement ``There exists a hollow red object'' using forward chaining.

Problem 2

Let A, B, C, D be Boolean random variables.

Given that:

Prob(A=T) = 0.8.
Prob(B=T | A=T) = 0.2
Prob(B=T | A=F) = 0.6
Prob(C=T | A=T) = 0.7
Prob(C=T | A=F) = 0.4
Prob(D=T | B=T) = 0.1
Prob(D=T | B=F) = 0.2
B and C are conditionally independent given A.
A and D are conditionally independent given B.

Evaluate the following expressions.