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Unformatted text preview: CSE541 EXERCISE 11 SOLUTIONS Chapters 10, 11, 12 Read and learn all examples and exercises in the chapters as well! QUESTION 1 Use the (complete) proof system GL from chapter 11 to prove that  = ( ( a b ) ( a b )) . Solution By completeness theorem for GL we have that  = A is and only if GL A . We construct a decomposition tree for our formula as follows. T A ( ( a b ) ( a b ))  ( ) ( a b ) ( a b )  ( ) ( a b ) a,b  ( ) a, ( a b ) b  ( ) a ( a b ) ,b ^ ( ) a a,b axiom a b,b  ( ) a,b b axiom All leaves are axioms, hence the tree is a proof of A in GL . QUESTION 2 Find a countermodel determined by a decomposition tree T A in GL for a formula A below. A = (( a b ) ( a b )) 1 Solution: We construct a decomposition tree for A formula as follows....
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 Spring '08
 Bachmair,L
 Computer Science

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