COS-451: ARTIFICIAL INTELLIGENCE
Final Project Version 3
Complete and submit the following final project problems and essay questions during the last
week of the semester. They cover material assigned in Modules 4 and 5 of the course, although
you will be expected to be able to make reference to material covered before the Midterm exam
as well. The points allotted for each item are given next to the item.
1. (10 points) Prove the following, using a truth table:
¬(P ∨ Q) ≡ (¬Q → ¬P)
2.
(20 points) Prove the following by using (a) truth tables and (b) the Resolution Rule: (Hint:
Convert to clause form.)
((P → Q) ∧ (Q → R)) → (P → R)
3.
(20 points) Assume you have an expert system that has the following rules and facts:
Rule 1: If the alarm beeps, there is smoke.
Rule 2: If there is smoke and it is very hot, you would conclude that there is a fire.
Rule 3: If there is a fire, then turn on the sprinkler system.
Fact 1: The alarm beeps.
Fact 2: It is very hot.
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 the sprinklers are turned on. (Assume that the
sprinklers are not turned on and arrive at a contradiction.)
d.
Use backward chaining to prove that the sprinklers are turned on.
4.
(20 points) Describe the Turing test and provide your opinion about whether it supports
Strong AI or Weak AI. Please make sure you define your terms.
5.
(10 points) Do you feel that search methods that you covered before the midterm exam
are relevant to the material you covered after the midterm? If yes, please explain why and how.
Specifically, describe how search methods would be used for rule-based systems, expert
systems, resolutions, theorem proving, etc.
6.
(10 points) Translate the following into English where A(x) means student x likes Artificial
Intelligence and B(x) means student x is intelligent. (Hint: Note that B(x) is not a typographical
error.)
a.
¬(∃x) A(x) ≡ (∀x) ¬A(x)
b.
(∃x) A(x) ∧ (∃y) B(y) ≡ (∃x) (∃y) (A(x) ∧ B(y))
7.
a.
b.
(10 points) If love (y, x) means that x love y, write in logic notation using ∃'s and ∀'s:
Everyone is loved by someone.
Someone is loved by everyone.
When preparing your answers, please identify each item clearly by item number and, where
appropriate, item letter. Be sure to include your name at the top of the paper, as well as the
course name and code and the semester and year in which you are enrolled.
If you use any text, online, or other sources as you prepare these problems and essays, be sure
to give appropriate credit to the source.