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a
c
b
Fig. 1. Sample argumentation framework from Dung [9]
- S is conflict-free if
α, β
S, α
β/
∈R
;
- an argument α
S is acceptable w.r.t S if
β
∈A
s.t. β
α
∈R
,
γ
S
;
- S is an admissible extension if S is conflict-free and all its arguments are
acceptable w.r.t. S ;
- S is a complete extension if S is admissible and ∀α ∈A\S , ∃β ∈ S s.t.
β → α ∈R .
s.t. γ
β
∈R
In the words of Dung, abstract argumentation formalizes the idea that, in a
debate, the one who has the last word laughs best. Consider again the very
simple AF in Figure 1 and a credulous semantic like the complete semantic,
which states that a valid extension is the one which includes all the arguments
that it defends. It is easy to see that
is a complete extension. a is attacked
by b , but since c attacks b and does not receive any attack, c defends a , i.e. a is
reinstated.
Our agents use a simulated dialogue process, introduced in [15], to exchange
similar attacks between their AF s. A simulated dialogue
{
a, c
}
starts with an “invi-
tation to discuss” from A (communicator) to B (addressee), by picking a random
argument σ in her own extension. If B evaluates σ as coherent with her own AF ,
the dialog stops: A and B already “agree”. On the contrary, if σ is not included
in any of B 's extensions, B faces an alternative: if she trusts A , she will revise her
own opinions (i.e., by adding the new information to her AF and by updating
her extensions); if instead B does not trust A , she will rebut α against σ and
wait for a reaction from A . The exchange between A and B continues until one
of the agents changes her mind (agreement is thus reached), or if both agents
leave the dialogue because neither is persuaded.
For the sake of generality, we left several choice points open. Mainly, we do
not commit to any specific argumentation semantics and we do not commit to
any specific opinion revision mechanism. We also assume that agents rely on
a trust model. Arguably, a realistic model of trust would to take into account
the authoritativeness , rank and social status of the interlocutor [26]. To date,
our dialogue model is orthogonal to trust, we define trust thresholds statically
but different trust models can be accommodated in the future. Furthermore, in
our model information is either accepted or rejected. Argumentative frameworks
can handle situations in which human beings partially accept information by
means of weighted argumentative frameworks [7] where a certain level of in-
consistency between arguments is tolerated. Such argumentation semantics are
called conflict-tolerant, whereby arguments in the same extension may attack
each other [3]. Again, for the sake of simplicity, we use conflict-free semantics.
D
 
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