Question

Consider the following logic problem:

If you like checkers, then you like chess.
If like computers, then you like coding.
If you like chess and you like coding, then you will learn AI. If you learn AI, you will be rich and famous.
You like checkers.
You like computers.
Prove that you will be rich.

1. We will solve this problem using propositional logic. First, show one propositional logic sentence for each of the first six sentences in the above problem. You may only draw from the following atomic sentences.

   • Like(Checker）• Like(Chess)• Like(Computers)• Like(Coding)• Learn(AI)• Rich• Famous

2. Convert each of the six sentences from part (a) into Conjunctive Normal Form (CNF). You may just show the final result for each sentence; no need to show the intermediate steps. Number your clauses.

3. Perform a resolution proof by refutation to prove you will be Rich, using the knowledge base from part (b). For each resolution step, show the numbers of the clauses used, the resulting clause, and then number the resulting clause.

4. What one literal (other than ¬Famous) could you add to the knowledge base in part (b) in order to prove ¬Famous using resolution proof by refutation?

Answer 1

3. Like(Chess) ^ Like(Coding) -> Learn(AI) = ¬( Like(Chess) ^ Like(Coding)) ∨ Learn(AI)

= ¬Like(Chess) ∨ ¬Like(Coding) ∨ Learn(AI)

4. Learn(AI) -> Rich ^ Famous = ¬Learn(AI) ∨ (Rich ^ Famous)

= (¬Learn(AI) ∨ Rich) ^ (¬Learn(AI) ∨ Famous)

5. Like(Checkers)

6. Like(Computers)

Correction in the last step, step numbers are 7,13 instead of 7,14

d) In order to prove ¬Famous, we can add ¬Learn(AI) in the knowledge base and then we cannot resolve ¬Learn(AI) ∨ Famous as there will be no Learn(AI) clause.