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In-Depth Information
• the decision language
DL
distinguishes
-
a set of
goals
. This set of literals
identifiesvariousgoalsasthecost(
cheap
or
expensive
), the quality of service (
good
or
bad
) and the availability (
slow
or
fast
),
-
a set of
decisions
G
=
{
cheap
,
expensive
,
fast
,
slow
,
bad
,
good
}
D
=
{
s
(
x
)
|
x
∈{
a
,
b
,
c
,
d
}}
. This set of literals identifies different
alternatives,
-
a set of
beliefs
, i.e. a set of literals identifying various features
Price
(
x
,
y
)
,
Resolution
(
∈{
high
,
low
}
(which means that y is the level of a certain feature of x) and a set of literals identifying the
possible replies of the responders
x
,
y
)
and
DeliveryTime
(
x
,
y
)
with x
∈{
a
,
b
,
c
,
d
}
,y
{
reply
(
)
|
∈{
accept
,
reject
}}
y
y
;
P
• the set of presumptions
sm contains the possible replies;
• the incompatibility relation
I
is trivially defined. In particular,
reply
(
accept
)
I
reply
(
reject
)
,
reply
(
reject
)
I
reply
(
accept
)
,and
s
(
)
I
s
(
)
=
y
good
I
bad
,
bad
I
good
,
expensive
I
cheap
,
cheap
I
expensive
,
slow
I
fast
,
fast
I
slow
;
• the theory
x
y
,withx
T
(whatever the agent is the buyer or the seller) is the set of rules shown in Table 2;
• the preferences of the buyer in our example are such that:
fast
P
cheap
and
fast
P
good
;
• The reservation value of the buyer is defined as:
RV
=
{
fast
}
. If the agent is the seller, then the
reservation value is defined as :
RV
=
{
}
.
expensive
(
x
)
:
expensive
←
s
(
x
)
,
Price
(
x
,
high
)
,
reply
(
accept
)
r
11
(
x
)
:
cheap
←
s
(
x
)
,
Price
(
x
,
low
)
,
reply
(
accept
)
r
12
(
x
)
:
good
←
s
(
x
)
,
Resolution
(
x
,
high
)
,
reply
(
accept
)
r
21
r
22
(
x
)
:
bad
←
s
(
x
)
,
Resolution
(
x
,
low
)
,
reply
(
accept
)
(
x
)
:
fast
←
(
x
)
,
DeliveryTime
(
x
,
low
)
,
reply
(
)
r
31
s
accept
r
32
(
x
)
:
slow
←
s
(
x
)
,
DeliveryTime
(
x
,
high
)
,
reply
(
accept
)
f
11
:
Price
(
a
,
high
)
←
f
12
:
Resolution
(
a
,
low
)
←
f
13
:
DeliveryTime
(
a
,
high
)
←
f
21
:
Price
(
b
,
high
)
←
f
22
:
Resolution
(
b
,
high
)
←
f
23
:
DeliveryTime
(
b
,
high
)
←
f
31
:
Price
(
c
,
high
)
←
f
32
:
Resolution
(
c
,
low
)
←
f
33
:
DeliveryTime
(
c
,
low
)
←
f
41
:
Price
(
d
,
low
)
←
f
42
:
Resolution
(
d
,
low
)
←
f
43
:
DeliveryTime
(
d
,
low
)
←
Table 2. The rules of the agents
Our formalism allows to capture the incomplete representation of a decision problem with
presumable beliefs. Arguments are built upon these incomplete statements.
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