This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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....
View
Full
Document
This note was uploaded on 02/12/2011 for the course CSE 541 taught by Professor Bachmair,l during the Spring '08 term at SUNY Stony Brook.
 Spring '08
 Bachmair,L
 Computer Science

Click to edit the document details