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:
H-Implication
⇒
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