CSE541
EXERCISE 3
SOLVE ALL PROBLEMS as PRACTICE and only AFTER look at the SOLUTIONS!!
Reminder:
We define
H
semantics operations
∪
and
∩
as follows
a
∪
b
=
max
{
a, b
}
,
a
∩
b
=
min
{
a, b
}
.
The Truth Tables
for Implication and Negation are:
HImplication
⇒
F
⊥
T
F
T
T
T
⊥
F
T
T
T
F
⊥
T
H Negation
¬
F
⊥
T
T
F
F
QUESTION 1
We know
that
v
:
V AR
→ {
F,
⊥
, T
}
is such that
v
*
((
a
∩
b
)
⇒
(
a
⇒
c
)) =
⊥
under
H
semantics.
evaluate
v
*
(((
b
⇒
a
)
⇒
(
a
⇒ ¬
c
))
∪
(
a
⇒
b
)).
QUESTION 2
We define
a 4 valued
ˆL
4
logic semantics as follows. The language is
L
=
L
{¬
,
⇒
,
∪
,
∩}
.
The logical connectives
¬
,
⇒
,
∪
,
∩
of
ˆL
4
are operations in the set
{
F,
⊥
1
,
⊥
2
, T
}
, where
{
F <
⊥
1
<
⊥
2
< T
}
,
defined as follows.
Negation
¬
is a function
¬
:
{
F,
⊥
1
,
⊥
2
, T
} → {
F,
⊥
1
,
⊥
2
, T
}
,
such that
¬⊥
1
=
⊥
1
,
¬⊥
2
=
⊥
2
,
¬
F
=
T,
¬
T
=
F.
Conjunction
∩
is a function
∩
:
{
F,
⊥
1
,
⊥
2
, T
} × {
F,
⊥
1
,
⊥
2
, T
} → {
F,
⊥
1
,
⊥
2
, , T
}
, such that for any
a, b
∈ {
F,
⊥
1
,
⊥
2
, T
}
,
a
∩
b
=
min
{
a, b
}
.
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Disjunction
∪
is a function
∪
:
{
F,
⊥
1
,
⊥
2
, T
} × {
F,
⊥
1
,
⊥
2
, T
} → {
F,
⊥
1
,
⊥
2
, T
}
, such that for any
a, b
∈ {
F,
⊥
1
,
⊥
2
, T
}
,
a
∪
b
=
max
{
a, b
}
.
Implication
⇒
is a function
⇒
:
{
F,
⊥
1
,
⊥
2
, T
} × {
F,
⊥
1
,
⊥
2
, T
} → {
F,
⊥
1
,
⊥
2
, T
}
,
such that for any
a, b
∈ {
F,
⊥
1
,
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 Bachmair,L
 Computer Science, Logic, Logical connective, Propositional calculus, L4 logic semantics

Click to edit the document details