Information Technology Reference
In-Depth Information
expensive
←
s
(
x
)
,
Price
(
x
,
high
)
,
reply
(
accept
)
,
∼
deleted
(
r
11
(
x
))
cheap
←
s
(
x
)
,
Price
(
x
,
low
)
,
reply
(
accept
)
,
∼
deleted
(
r
12
(
x
))
good
←
s
(
x
)
,
Resolution
(
x
,
high
)
,
reply
(
accept
)
,
∼
deleted
(
r
21
(
x
))
bad
←
s
(
)
,
Resolution
(
x
,
low
)
,
reply
(
accept
)
∼
deleted
(
r
22
(
))
x
,
x
fast
←
s
(
)
,
DeliveryTime
(
x
,
low
)
,
reply
(
accept
)
∼
deleted
(
r
31
(
))
x
,
x
slow
←
s
(
)
,
DeliveryTime
(
x
,
high
)
,
reply
(
accept
)
∼
deleted
(
r
32
(
))
x
,
x
Price
(
a
,
high
)
←∼
deleted
(
f
11
)
Resolution
(
a
,
low
)
←∼
deleted
(
f
12
)
DeliveryTime
(
a
,
high
)
←∼
deleted
(
f
13
)
Price
(
b
,
high
)
←∼
deleted
(
f
21
)
Resolution
(
b
,
high
)
←∼
deleted
(
)
f
22
DeliveryTime
(
b
,
high
)
←∼
deleted
(
)
f
23
Price
(
c
,
high
)
←∼
deleted
(
)
Resolution
(
c
,
low
)
←∼
deleted
(
f
31
)
f
32
DeliveryTime
(
c
,
low
)
←∼
deleted
(
f
33
)
Price
(
d
,
low
)
←∼
deleted
(
)
Resolution
(
d
,
low
)
←∼
deleted
(
f
41
f
42
)
(
d
,
low
)
←∼
(
f
43
)
DeliveryTime
deleted
Table 3. The rules of the PABF
There is a one-to-one mapping between arguments in our AF and arguments in some
corresponding PABFs.
Lemma 1
(Mapping between arguments)
.
Let
DF
=
DL
,
P
sm
,
I
,
T
,
P
,
RV
be a decision framework,
G
∈G
a set of goals and
PABFS
DF
(
G
)
be
the set of PABFs associated with the goals
G
.
1. Given a structured argument built upon
DF
concluding
α
∈DL
, there is a corresponding argument
deducing
α
in some PABFs of
PABFS
(
G
)
.
2. Given an atomic formula
α
∈DL
and an argument of a PABF in
PABFS
(
G
)
deducing
α
,there
exists a corresponding structured argument in
A
(
DF
)
concluding
α
.
Let us consider the previous example.
Example 10
(Assumptions)
.
The arguments in some PABFs corresponding to the structured
arguments D
2
and C include the following set of assumptions:
•
D
2
)=
{∼
deleted
(
r
31
(
d
))
(
∼
deleted
(
f
43
)
,
s
(
d
)
,
reply
(
accept
)
}
,
;
C
(
)=
{∼
deleted
(
r
31
(
c
))
∼
deleted
(
f
33
)
,
s
(
c
)
,
reply
(
accept
)
}
•
,
;
D
2
)
(
Both of them are tree argument. The corresponding set of assumptions
considers the literals
since D
2
is built upon these rules. Moreover, the literal
∼
deleted
(
r
31
(
d
))
∼
deleted
(
f
43
)
and
s
(
d
)
(respectively
reply
(
accept
)
) is a decision literal (respectively a presumption).
In order to compute our extension-based semantics, we explore the collection of PABFs
associated to our AF in order to find the PABF which deduces the strongest goals as possible.
Indeed, we have developed a mechanism to explore the collection of PABFs associated to our
AF in order to compute it. If a s-admissible set of structured arguments concludes some goals,
then there is a corresponding admissible set of assumptions in one of the corresponding PABFs
and there is no other PABF, where an admissible set of assumptions deduces stronger goals.
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