Information Technology Reference
In-Depth Information
A
1
,...,
A
n
A
The set of structured arguments
{
}
is denoted by
sbarg
(
)
, and its elements are
called the
subarguments
of A.
The set of arguments built upon
DF
is denoted by
.
Notice that the subarguments of a tree argument concluding the weak literals are hypothetical
arguments. Indeed, the conclusion of an hypothetical argument could be a strong or a weak
literal, while the conclusion of a built argument is a strong literal. As in (Vreeswijk, 1997),
we consider composite arguments, called
tree
arguments, and atomic arguments, called
trivial
arguments. Unlike the other definitions of arguments (set of assumptions, set of rules), our
definition considers that the different premises can be challenged and can be supported by
subarguments. In this way, arguments are intelligible explanations. Moreover, we consider
hypothetical
arguments which are built upon missing information or a suggestion, i.e. a
decision. In this way, our framework allows to reason further by making suppositions related
to the unknown beliefs and over possible decisions.
Let us consider the previous example.
Example 4
(Arguments)
.
The arguments D
2
and
¯
Cconcluding
fast
are depicted in Fig. 1 and Fig. 2, respectively. They are arguments concluding that the availability
is promoted since the delivery time of the services
c
and
d
is low. For this purpose we need to suppose
that the seller's reply will be an acceptance. An argument can be represented as a tree where the
root is the conclusion (represented by a triangle) directly connected to the premises (represented by
losanges) if they exist, and where leaves are either decisions/presumptions (represented by circles) or
the unconditionally true statement. Each plain arrow corresponds to a rule (or a fact) where the head
node corresponds to the head of the rule and the tall nodes represent the literals in the body of the rule.
Thetreearguments
¯
Cand D
2
are composed of three subarguments: two hypothetical and one trivial
argument. Neither trivial arguments nor hypothetical arguments contain subarguments.
A
(
DF
)
3.4 Interactions between arguments
In order to turn the decision framework into an argumentation framework, we need to capture
the interactions between arguments. The interactions amongst structured arguments may
come from their conflicts and from the priority over the goals which are promoted by these
arguments. We examine in turn these different sources of interaction. Firstly, we define the
attack relation amongst conflicting structured arguments in the same way we have defined
the attack relation in the assumption-based argumentation frameworks. Secondly, we define
the strength of arguments. Finally, we define the defeat relation amongst the structured
arguments to capture the whole of interactions amongst them.
Since their sentences are conflicting, the structured arguments interact with one another. For
this purpose, we define the following attack relation.
Definition 11
(Attack relation)
.
Let
DF
=
DL
,
P
sm
,
I
,
T
,
P
,
RV
be a decision framework, and
A
,
B
be two structured arguments. A
attacks
B iff
sent
(
A
B
.
This relation encompasses both the direct (often called
rebuttal
) attack due to the
incompatibility of the conclusions, and the indirect (often called
undermining
) attack, i.e.
directed to a “subconclusion”. According to this definition,
∈A
(
DF
)
)
I
sent
(
)
if an argument attacks a
subargument, the whole argument is attacked.
Let us go back to our example.
Example 5
(Attack relation)
.
D
2
(respectively C) is built upon the hypothetical subargument
). Therefore,
¯
Cand D attack each other.
supposing
s
(
d
)
(respectively
s
(
c
)
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