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the state is
s
, and that the agent
i
believes state
s
may occurs. More
formally:
Definition 3.5 (Agent Potential Objection)
An agent
i
,given
the evidences
E
and a consequence
y
,
potentially objects to
aconse-
quence
x
using
y
,if
y
i,B
i
x
holds, where
B
i
is the opinion of agent
i
.
Example 3.13
Consider again the preference of agent
A
3
in Exam-
ple 3.5. Given evidences
E
=
{
(Director = Spielberg)
∧
(Type = S.F)
}
,
agent
A
3
potentially objects to
x
2
using
x
1
, and it also potentially
objects to
x
1
using
x
2
. In this case we see that both
x
2
3
,{
Good
,
Average
}
x
1
and
x
1
3
,{
Good
,
Average
}
x
2
hold.
Example 3.14
Consider agent
A
1
in Example 3.5. Since
E
=
{
(Director = Spielberg)
∧
(Type = S.F)
},
according to his own experience
I
1
(Example 3.5), agent
A
1
has the
opinion
B
1
=
O
1
(
E,I
1
)=
{
Good
}
.
Assume that the preference rules
P
1
of agent
A
1
are as follows:
P1.
{
Good
}⇒
x
2
1
x
1
P2.
{
Average
}⇒
x
2
1
x
1
x
1
1
x
2
P4.
{
Good
,
Average
}⇒x
2
1
x
1
then we know that agent
A
1
definitely objects to
x
1
using
x
2
because
x
2
1
,{
Good
}
x
1
holds, but not
x
1
1
,{
Good
}
x
2
.
P3.
{
Bad
}⇒
We see that by Definitions 3.4 and 3.5, if an agent definitely objects
to
y
using
x
, then formally he also potentially objects to
y
using
x
.
However, intuitively this 'potentiality' is actually very definite, so it is
not too interesting to us.
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