exercise6

# exercise6 - with axiom A1 i.e such that A 1 = A 1 2 Use...

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CSE541 EXERCISE 6 SOLVE ALL PROBLEMS as PRACTICE and only AFTER look at the SOLUTIONS!! QUESTION 1 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 )) 1. Prove that S is sound under classical semantics. 2. Determine whether S is sound or not sound under K semantics. K semantics diﬀer from ˆLukasiewicz’s semantics only in a case on implication only. This table is: K-Implication F T F T T T ⊥ ⊥ T T F T QUESTION 2 1. Write a formal proof A 1 ,A 2 ,A 3 in S from the QUESTION 3 with 2 applications of the rule ( r ) that starts
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Unformatted text preview: with axiom A1, i.e such that A 1 = A 1. 2. Use results from QUESTION 3 to determine whether | = K A 3 . 3. Write a formal proof A 1 ,A 2 in S from the QUESTION 3 with 1 application of the rule ( r ) that starts with axiom A2, i.e such that A 1 = A 2. 4. Use results from QUESTION 1 to determine whether | = A 2 . QUESTION 3 Prove, by constructing a formal proof in S from the QUESTION 1 that ‘ S ( A ⇒ ( A ⇒ ( A ⇒ ( A ⇒ A )))) . 1...
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