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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 counter-model 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
- Computer Science