exercise10

exercise10 - CSE541 EXERCISE 10 Covers Chapters 10, 11, 12...

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CSE541 EXERCISE 10 Covers Chapters 10, 11, 12 Read and learn all examples and exercises in the chapters as well! QUESTION 1 Let GL be the Gentzen style proof system for classical logic deﬁned in chapter 11. Prove, by constructing a proper decomposition tree that (1) GL (( ¬ a b ) ( ¬ b a )). (2) 6 ‘ GL (( a b ) ( ¬ b a )) . QUESTION 2 Show that tree below do not constitute a proof in GL deﬁned in chapter 11. T A -→ ¬¬ (( ¬ a b ) ( ¬ b a )) | ( → ¬ ) ¬ (( ¬ a b ) ( ¬ b a )) -→ | ( ¬ → ) -→ (( ¬ a b ) ( ¬ b a )) | ( →⇒ ) ( ¬ a b ) -→ ( ¬ b a ) | ( →⇒ ) ( ¬ a b ) , ¬ b -→ a | ( ¬ → ) ( ¬ a b ) -→ b,a ^ ( ⇒-→ ) -→ ¬ a,b,a | ( → ¬ ) a -→ b,a axiom b -→ b,a axiom 1

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QUESTION 3 Let GL be the Gentzen style proof system for classical logic deﬁned in chapter 11. Prove, by constructing a counter-model deﬁned by a proper decomposition tree that 6| = (( a ( ¬ b a )) ( ¬ b ( a b ))) . QUESTION 4 Consider a system RS1 obtained from RS by changing the sequence Γ
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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.

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exercise10 - CSE541 EXERCISE 10 Covers Chapters 10, 11, 12...

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