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level, or there exists a more important level where
b
satisfies more interests than
a
.
This means that any argument with conclusion
pref
(
a
,
b
)
(which has to be of the form
above) is either undercut by
count
(
b
,
[
P
]
,
S
)
uc
because it uses a non-maximal count, or
by
prefinf
(
a
,
b
,
[
P
])
uc
because there is a more important level where a preference for
b
over
a
can be derived. This means that any such argument will not be sceptically
justified.
(ii)
: Suppose
a
is strictly ceteris paribus preferred over
b
. This means that there is (at
least) one interest, let us say
P
,that
a
satisfies and
b
does not, and there are no interests
that
b
satisfies and
a
does not. In this case, we can construct the following argument.
⇐
P
(
a
)
I
(
P
)
sat
(
a
,
[
P
]
,
1
)
sat
(
b
,
[
P
]
,
0
)
P
≈
P
1
>
0
pref
(
a
,
b
)
Premise
P
(
a
)
is justified by condition 1.2. Premise
I
(
P
)
cannot be defeated (condition
1.1). Note that, since there is no importance ordering specified, counts can only include
0 or 1 interest(s). So the first count cannot be undercut, because there are no other
interests that are equally important as
P
(condition 1.3b). The second count cannot be
undercut because
b
does not satisfy
P
. Since there are no interests that
b
satisfies but
a
does not, the last inference can only be undercut by an undercutter that uses a non-
maximal count and so will be undercut itself.
⇒
: Suppose
a
is not strictly ceteris paribus preferred over
b
. This means that either there
is no interest that
a
satisfies but
b
does not, or there is some interest that
b
satisfies and
a
does not. In the first case, the only arguments that derive a preference for
a
over
b
have
to use non-maximal counts and hence are undercut. In the second case, any argument
that derives a preference for
a
over
b
is rebut by the following argument,
Q
(
b
)
I
(
Q
)
sat
(
b
,
[
Q
]
,
1
)
sat
(
a
,
[
Q
]
,
0
)
Q
≈
Q
1
>
0
pref
(
b
,
a
)
and is not sceptically justified.
7
Conclusions
In this paper we have made a case for explicitly modelling underlying interests when
reasoning about preferences in the context of practical reasoning. We have presented
an argumentation framework for reasoning about qualitative interest-based preferences
that models ceteris paribus and lexicographic preference.
In the current framework, we have only considered Boolean issues and interests.
While this suffices to illustrate the main points discussed in this paper, multi-valued
scales would be more realistic. Such an approach would open the way to modelling dif-
ferent degrees of (dis)satisfaction of an interest. For example, [5] take into account the
level of satisfaction of goals on a bipolar scale. In the Boolean case, the lexicographic
preference ordering is based on counting the number of interests that are satisfied by
outcomes. This is no longer possible if multi-valued scales are used. In that case, we
