Timothy Martens
ARTIFICIAL INTELLIGENCE
COS 451 OL009 September 2008
1.
(10 points)
Prove the following, using a truth table:
A
∨
(
A
∧
B
)
≡
A
A
B
A
∨
(
A
∧
B
)
≡
A
T
T
T
T
F
T
F
T
F
F
F
F
2.
(20 points)
Prove the following by using (a) truth tables and (b) the Resolution
Rule: (Hint: Convert to clause form.)
P
∧
(Q ↔ P)) → Q
(a)
P
Q
P
∧
(Q ↔ P)) → Q
T
T
T
T
F
F
F
T
T
F
F
F
(b)
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∧
(Q ↔ P)) → Q
P
∧
(Q
∨
P)
∧
(¬Q
∨
¬P)
{(p),(Q,P),( ¬Q ,¬P)}
{(p)}
3.
(20 points)
Assume you have an expert system that has the following rules and
facts:
Rule 1:
Walking on air when dating someone implies that you are in love with
that person.
Rule 2:
If you are in love with that person and you want to start a family, you will
be getting married.
Rule 3:
If you are getting married, you will burn your black book.
Fact 1:
You are walking on air when dating someone.
Fact 2:
You want to start a family.
a.
Convert these rules and facts into logic notation and then into clause notation.
b.
Provide 2 additional facts that can be deduced. (Use forward chaining.)
c.
Use proof by refutation to conclude that you will burn your black book. (Assume
that you will not burn your black book and arrive at a contradiction.)
d.
Use backward chaining to prove that you will be burning your black book.
X = 1
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 Summer '09
 JasonLitz
 Artificial Intelligence, Forward chaining, black book

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