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The set of arguments built upon
.
In an assumption-based argumentation framework, the attack relation amongst arguments
comes from the contrary relation.
A
sm
is denoted
A
(
A
sm
)
Definition 7
(Attack relation)
.
An argument
a
:
A
α
attacks
an argument
b
:
B
β
iffthereisan
assumption x
∈
B
such as
α
∈C
on
(
x
)
.
According to the two previous definitions, an ABF is clearly a concrete instantiation of an AAF
where arguments are deductions and the attack relation comes from the contrary relation.
Example 2
(ABF)
.
Let
abf
=
L
,
R
,
A
sm
,
C
on
be an assumption-based argumentation framework
where:
•
(
L
R
)
,
is a deductive system where,
L
=
{α
¬α
¬β
¬δ
¬γ}
-
,
β
,
δ
,
γ
,
,
,
,
,
R
-
is the following set of rules,
¬
α
←
α
¬
α
←
β
¬
β
←
α
¬
γ
←
δ
¬
δ
←
γ
•
A
sm
=
{
α
,
β
,
γ
,
δ
}
. Notice that no assumption is the head of an inference rule in
R
;
•and
C
on
(
α
)=
{¬
α
}
,
C
on
(
β
)=
{¬
β
}
,
C
on
(
γ
)=
{¬
γ
}
,and
C
on
(
δ
)=
{¬
δ
}
.
Some of the arguments in
abf
are the following:
{
α
}¬
α
{
α
}¬
β
{
β
}¬
α
{
γ
}¬
δ
{
δ
}¬
γ
As stated in Dung et al. (2007), this ABF is a concrete instance of the AAF example proposed previously.
3. Proposal
This section presents our framework to perform decision making. Taking into account its
goals and preferences, an agent needs to solve a decision-making problemwhere the decision
amounts to an alternative it can select even if some goals cannot be reached. This agent uses
argumentation in order to assess the suitability of alternatives and to identify “optimal” ones.
It argues internally to link the alternatives, their features and the benefits that these features
guarantee under possibly incomplete knowledge.
We present here the core of our proposal, i.e. an argumentation framework for decision
making. Section 3.1 introduces the walk-through example. Section 3.2 introduces the
framework used to capture decision problems. Section 3.3 defines the arguments. Section 3.4
defines the interactions amongst our arguments. Section 3.5 defines our AF. Finally, Section 3.6
presents its computational counterpart.
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