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Unformatted text preview: CSE541 EXERCISE 9 Problem 1 H is the following proof system: H = ( L {⇒} , F , AX = { A 1 ,A 2 } , MP ) A1 ( B ⇒ ( A ⇒ B )) , A2 (( B ⇒ ( A ⇒ C )) ⇒ (( B ⇒ A ) ⇒ ( B ⇒ C ))) , MP (Rule of inference) ( MP ) A ; ( A ⇒ B ) B (1) Prove that H is SOUND under classical semantics. (2) Does Deduction Theorem holds for H ? Justify. (3) Is H COMPLETE with respect to all classical semantics tautologies? Justify. Problem 2 Here are consecutive steps B 1 ,...,B 9 in a proof of (( B ⇒ A ) ⇒ ( ¬ A ⇒ ¬ B )) in H 2 of our Book. The comments included are incomplete. Complete the comments by writing all details. You have to write down the proper substitutions and for mulas used at each step of the proof. B 1 = ( B ⇒ A ) Hypothesis B 2 = ( ¬¬ B ⇒ B ) Already proved formula: ( ¬¬ A ⇒ A ) for B 3 = ( ¬¬ B ⇒ A ) Already proved fact: ( A ⇒ B ) , ( B ⇒ C ) ‘ H 2 ( A ⇒ C ) B 4 = ( A ⇒ ¬¬ A ) 1 B 5 = ( ¬¬ B ⇒ ¬¬ A ) Already proved fact: ( A ⇒ B ) , (...
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This note was uploaded on 02/12/2011 for the course CSE 541 taught by Professor Bachmair,l during the Spring '08 term at SUNY Stony Brook.
 Spring '08
 Bachmair,L
 Computer Science

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