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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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