Information Technology Reference
In-Depth Information
Ta b l e 3 .
The knowledge base for the example
highsal
(
c
)
I
M
(
wealth
)
highsal
(
x
)
⇒
wealth
(
x
)
¬
highpos
(
c
)
I
M
(
status
)
highsal
(
x
)
⇒
status
(
x
)
full-time
(
c
)
I
M
(
family
)
highpos
(
x
)
⇒
status
(
x
)
¬
highsal
(
f
)
¬
full-time
(
x
)
⇒
family
(
x
)
highpos
(
f
)
I
J
(
manager
)
highpos
(
x
)
⇒
manager
(
x
)
¬
full-time
(
f
)
I
J
(
cutback
)
¬
highsal
(
x
)
⇒
cutback
(
x
)
combination, which in this case is defined by being neither too colourless nor too flashy.
The satisfaction of this interest by the different outcomes is listed in Table 2b. The vari-
ables jacket and pants are unconditional, so they can remain as criteria. If we take jacket,
pants, and good combination as criteria, we can construct the preference graph in Figure
2b, using the ceteris paribus principle. The difference with the preferences induced by
the CP-net is that in the CP-net case, outcome
i
is more preferred than
k
and
m
,and
p
is
less preferred than
l
and
n
, while in the interest-based case they are incomparable. This
is due to the fact that in CP-nets, conditional preferences are implicitly considered less
important than the preferences on the variables they depend on ([16], p. 145). In fact,
if we would specify that both jacket and pants are more important than a good com-
bination, our preference ordering would be the same as in Figure 2a. But the interest
approach is more flexible; it is possible to specify any (partial) importance ordering on
interests. For example, we could also state that a good combination is more important
than either the jacket or the pants, which results in the preference ordering in Figure 2c.
In our opinion, there is no a priori reason to attach more importance to unconditional
variables as is done in the CP-net approach.
6
Argumentation Framework
In this section, we present an argumentation framework (AF) for reasoning about qual-
itative, interest-based preferences. An abstract AF in the sense of Dung [11] is a pair
A
is a defeat relation (informally, a coun-
terargument relation) among those arguments. To define which arguments are justified,
we use Dung's [11] preferred semantics.
,
→
where
A
is a set of arguments and
→
Definition 2. (Preferred Semantics) .
A
preferred extension
of an AF
A
,
→
is a
maximal (w.r.t.
⊆
)set
S
⊆A
such that:
∀
A
,
B
∈
S
:
A
→
B
and
∀
A
∈
S
:if
B
→
A
then
∃
C
∈
S
:
C
B
. An argument is credulously (sceptically)
justified
w.r.t. preferred semantics
if it is in some (all) preferred extension(s).
→
Informally, a preferred extension is a coherent point of view that can be defended
against all its attackers. In case of contradictory information, there will be multiple
preferred extensions, each advocating one point of view. The contradictory conclusions
will be credulously, but not sceptically justified.
We instantiate an abstract AF by specifying the structure of arguments and the defeat
relation.
