exercise7

# exercise7 - r that starts with axiom A1 i.e such that A 1 =...

This preview shows pages 1–2. Sign up to view the full content.

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 (

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

exercise7 - r that starts with axiom A1 i.e such that A 1 =...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online