exercise12 - 6| = (( a ( b a )) ( b ( a b ))) . QUESTION 4...

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CSE541 EXERCISE 12 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 10? Provide a correct proof. 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
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Unformatted text preview: 6| = (( a ( b a )) ( b ( a b ))) . QUESTION 4 Let LI be the Gentzen system for intuitionistic logic as dened in chapter 11. Show that LI (( a b ) ( b a )) . QUESTION 5 We know that the formulas below are not Intuitionistic Tautologies. Verify whether H seman-tics (chapter 5) provides a counter-model for them. (( a b ) ( a b )) , (( a b ) ( b a )) . QUESTION 6 Show that LI (( a b ) ( b a )) QUESTION 7 Use the heuristic method dened in chapter 12 to prove that 6 LI (( a b ) ( b a )) . 2...
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exercise12 - 6| = (( a ( b a )) ( b ( a b ))) . QUESTION 4...

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