12 PS3 - 1 Handout #12 April 12, 2010 CS103 Robert Plummer...

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1 Handout #12 CS103 April 12, 2010 Robert Plummer Problem Set #3—Due Monday, 4/19 in class 1. Construct a proof by resolution that shows that the following CNF (conjunctive normal form) sentence is not satisfiable. Do so by drawing a resolution diagram as shown in class. If you can derive the empty clause (regardless of whether you still have other clauses left), then the sentence is not satisfiable. (A ¬ C B) ¬ A (C B A) (A ¬ B) A good strategy is to deal with unit clauses first. That is, pick a unit clause (if any), do all the resolutions you can with it, then pick another unit clause, etc. 2. Construct a resolution proof that shows that the following sentence is not satisfiable. Since the sentence is not in CNF, you will have to convert it to CNF first. ¬¬ A ( ¬ A (( ¬ B C) B)) ¬ C Note that if in creating the CNF you arrive at something like (A ¬ A), you should replace this with F, then use rules for simplifying expressions containing F, then proceed
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12 PS3 - 1 Handout #12 April 12, 2010 CS103 Robert Plummer...

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