CSE541
EXERCISE 10
Covers Chapters 10, 11, 12
Read and learn all examples and exercises in the chapters as well!
QUESTION 1
Let
GL
be the Gentzen style proof system for classical logic deﬁned in chapter 11. Prove, by constructing
a proper decomposition tree that
(1)
‘
GL
((
¬
a
⇒
b
)
⇒
(
¬
b
⇒
a
)).
(2)
6 ‘
GL
((
a
⇒
b
)
⇒
(
¬
b
⇒
a
))
.
QUESTION 2
Show that tree below do not constitute a proof in
GL
deﬁned in chapter 11.
T
→
A
→ ¬¬
((
¬
a
⇒
b
)
⇒
(
¬
b
⇒
a
))

(
→ ¬
)
¬
((
¬
a
⇒
b
)
⇒
(
¬
b
⇒
a
))
→

(
¬ →
)
→
((
¬
a
⇒
b
)
⇒
(
¬
b
⇒
a
))

(
→⇒
)
(
¬
a
⇒
b
)
→
(
¬
b
⇒
a
)

(
→⇒
)
(
¬
a
⇒
b
)
,
¬
b
→
a

(
¬ →
)
(
¬
a
⇒
b
)
→
b,a
^
(
⇒→
)
→ ¬
a,b,a

(
→ ¬
)
a
→
b,a
axiom
b
→
b,a
axiom
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentQUESTION 3
Let
GL
be the Gentzen style proof system for classical logic deﬁned in chapter 11. Prove, by constructing
a countermodel deﬁned by a proper decomposition tree that
6
= ((
a
⇒
(
¬
b
∩
a
))
⇒
(
¬
b
⇒
(
a
∪
b
)))
.
QUESTION 4
Consider a system
RS1
obtained from
RS
by changing the sequence Γ
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 Bachmair,L
 Computer Science, Logic, Mathematical logic, Proof theory, decomposition tree, Intuitionistic Tautologies, proper decomposition tree

Click to edit the document details