Question 6: CNF Consider the following KB with two formulas: $(p \supset q) \equiv r$, $(p \supset q) \equiv \neg r$. Answer the following questions: 1. (4 pts) Convert the KB to a set of clauses. 2. (4 pts) Use resolution to prove that the KB is contradictory. 8 points
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Converting the KB to a set of clauses: The given KB consists of two formulas: Show more…
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K S.
(a) Prove using resolution that the following sentence entails G: (A ∨ B) ∧ (¬ A ∨ C) ∧ (¬ B ∨ D) ∧ (¬ C ∨ G) ∧ (¬ D ∨ G) (b) Two clauses are semantically distinct if they are not logically equivalent. How many semantically distinct 2-CNF clauses can be constructed from n proposition symbols? (c) Using your answer to (b), prove that propositional resolution always terminates in time polynomial in n given a 2-CNF sentence containing no more than n distinct symbols. (d) Explain why your argument in (c) does not apply to 3-CNF.
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