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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.
(10 points) Prove the following, using a truth table:
A → B ≡ ¬A ∨ B
(20 points) Prove the following by using (a) truth tables and (b) the Resolution Rule: (Hint: Convert to clause form.)
((P ∨ Q) ∧ (P→R))∧ (R→S) → (Q ∨ S)
(20 points) Assume you have an expert system that has the following rules and facts:
Rule 1: A company not paying its bills implies that there are problems.
Rule 2: If there are problems and the CEO throws a billion dollar party, you conclude that irregularities exist.
Rule 3: If irregularities exist, then call the FBI to investigate.
Fact 1: The company is not paying its bills.
Fact 2: The CEO throws a billion dollar party.
Convert these rules and facts into logic notation and then into clause notation.
Provide 2 additional facts that can be deduced. (Use forward chaining.)
Use proof by refutation to conclude that the FBI is called in to investigate. (Assume that the FBI is not called in to investigate and arrive at a contradiction.)
Use backward chaining to prove that the FBI is called in to investigate.
(20 points) What relevance do the Chinese Room argument and the Turing test have to Strong AI and Weak AI? Please make sure you define your terms.
(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.
(10 points) Translate the following into English where A(x) means student x thinks Mozart is a great composer and B(x) means student x has good judgment. (Hint: Note that B(x) is not a typographical error.)
¬(∃x) A(x) ≡ (∀x) ¬A(x)
(∃x) A(x) ∧ (∃y) B(y) ≡ (∃x) (∃y) (A(x) ∧ B(y))
(10 points) Represent the following sentences in first-order logic, using a consistent vocabulary which you will define:
Some students took Artificial Intelligence.
Every Student who takes Artificial Intelligence passes it.
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.
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.
(10 points) Prove the following, using a truth table:
A → B ≡ ¬A ∨ B
(20 points) Prove the following by using (a) truth tables and (b) the Resolution Rule: (Hint: Convert to clause form.)
((P ∨ Q) ∧ (P→R))∧ (R→S) → (Q ∨ S)
(20 points) Assume you have an expert system that has the following rules and facts:
Rule 1: A company not paying its bills implies that there are problems.
Rule 2: If there are problems and the CEO throws a billion dollar party, you conclude that irregularities exist.
Rule 3: If irregularities exist, then call the FBI to investigate.
Fact 1: The company is not paying its bills.
Fact 2: The CEO throws a billion dollar party.
Convert these rules and facts into logic notation and then into clause notation.
Provide 2 additional facts that can be deduced. (Use forward chaining.)
Use proof by refutation to conclude that the FBI is called in to investigate. (Assume that the FBI is not called in to investigate and arrive at a contradiction.)
Use backward chaining to prove that the FBI is called in to investigate.
(20 points) What relevance do the Chinese Room argument and the Turing test have to Strong AI and Weak AI? Please make sure you define your terms.
(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.
(10 points) Translate the following into English where A(x) means student x thinks Mozart is a great composer and B(x) means student x has good judgment. (Hint: Note that B(x) is not a typographical error.)
¬(∃x) A(x) ≡ (∀x) ¬A(x)
(∃x) A(x) ∧ (∃y) B(y) ≡ (∃x) (∃y) (A(x) ∧ B(y))
(10 points) Represent the following sentences in first-order logic, using a consistent vocabulary which you will define:
Some students took Artificial Intelligence.
Every Student who takes Artificial Intelligence passes it.
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.
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