exercise7 - r ) that starts with axiom A1, i.e such that A...

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CSE451 EXERCISE 7 Problem 1 Given a proof system: S = ( L , ⇒} , E = F AX = { ( A A ) , ( A ( ¬ A B )) } , ( r ) ( A B ) ( B ( A B )) ) . 1. Prove that S is sound under classical semantics. 2. Prove that S is not sound under K semantics. 3. Write a formal proof in S with 2 applications of the rule ( r ). Problem 2 Prove, by constructing a formal proof that S (( ¬ A B ) ( A ( ¬ A B ))) , where S is the proof system from Problem 1. Problem 3 Given a proof system: S = ( L {∪ , ⇒} , E = F AX = { A 1 ,A 2 } , R = { ( r ) } ) , where A 1 = ( A ( A B )) , A 2 = ( A ( B A )) and ( r ) ( A B ) ( A ( A B )) Prove that S is sound under classical semantics. Problem 4 Determine whether S from the Problem 3 is sound or not sound under K semantics. Problem 5 Write a formal proof A 1 ,A 2 ,A 3 in S from the Problem 3 with 2 applications of the rule (
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Unformatted text preview: r ) that starts with axiom A1, i.e such that A 1 = A 1. 1 Problem 6 Use results from Problem 4 to determine whether | = K A 3 . Problem 7 Write a formal proof A 1 ,A 2 in S from the Problem 3 with 1 application of the rule ( r ) that starts with axiom A2, i.e such that A 1 = A 2. Problem 8 Use results from Problem 3 to determine whether | = A 2 . Problem 9 Prove, by constructing a formal proof in S from the Problem 3 that S ( A ( A ( A ( A A )))) . 2...
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exercise7 - r ) that starts with axiom A1, i.e such that A...

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