Information Technology Reference
In-Depth Information
Ta b l e 5 .
Example arguments
highsal
(
c
)
highsal
(
x
)
⇒
wealth
(
x
)
wealth
(
c
)
A
:
I
M
(
wealth
)
sat
(
c
,
[
wealth
]
M
,
1
)
sat
(
f
,
[
wealth
]
M
,
0
)
wealth
≈
M
wealth
1
>
0
α
B
¬
full-time
(
f
)
¬
full-time
(
x
)
⇒
family
(
x
)
family
(
f
)
pref
M
(
c
,
f
)
I
M
(
family
)
sat
(
f
,
[
family
]
M
,
1
)
sat
(
c
,
[
family
]
M
,
0
)
family
≈
M
family
1
>
0
β
C
highsal
(
c
)
highsal
(
x
)
⇒
wealth
(
x
)
wealth
(
c
)
pref
M
(
f
,
c
)
I
M
(
wealth
)
sat
(
c
,
[
wealth
]
M
,
1
)
sat
(
f
,
[
wealth
]
M
,
0
)
wealth
M
family
1
=
0
D
¬
full-time
(
f
)
¬
full-time
(
x
)
⇒
family
(
x
)
family
(
f
)
β
is inapplicable
I
M
(
family
)
sat
(
f
,
[
family
]
M
,
1
)
sat
(
c
,
[
family
]
M
,
0
)
family
M
wealth
1
=
0
α
isinapplicable
ϕ
∈L
KB
::
=
L
|
I
α
(
P
)
|
P
α
Q
|
P
≈
α
Q
|
L
1
,...,
L
k
,
∼
L
l
,...,
∼
L
m
⇒
L
n
where
L
i
=
P
(
a
)
or
¬
P
(
a
)
.
ψ
∈L
::
=
ϕ
∈L
KB
|∼
L
|
sat
(
a
,
[
P
]
α
,
n
)
|
pref
(
a
,
b
)
|
eqpref
(
a
,
b
)
α
α
We make a distinction between an input and full language. A knowledge base, which is
the input for an argumentation framework, is specified in the input language. The input
language allows us to express facts about the criteria that outcomes (do not) satisfy,
statements about interests of an audience and their importance ordering, and defeasible
rules. The knowledge base for the job contract example (the facts restricted to outcomes
c
and
f
) is displayed in Table 3. Other formulas of the language that are not part of the
input language, e.g. expressing a preference between two outcomes, can be derived
from a knowledge base using inference steps that build up an argument (such formulas
are not allowed in a knowledge base because they might contradict derived statements).
Inferences.
Table 4 shows the inference schemes that are used. The first inference
scheme is called defeasible modus ponens. It allows to infer conclusions from defea-
sible rules. The next two inference rules define the meaning of the weak negation
∼
.
According to inference rule 2, a formula
can always be inferred, but such an ar-
gument will be defeated by an undercutter built with inference rule 3 if
∼
ϕ
is the case.
Inference schemes 4 and 5 are used to count the number of interests of equal importance
(according to audience
ϕ
) as some interest
P
1
that outcome
a
satisfies. This type of in-
ference is inspired by accrual [18], which combines multiple arguments with the same
conclusion into one accrued argument for the same conclusion. Although our applica-
tion is different, we use a similar mechanism. Inference scheme 4 can be used when an
outcome satisfies no interests. It is possible to construct an argument that does not count
all interests that are satisfied, a so-called non-maximal count. But we want all interests
α
