Arguing over Goals for Negotiation: Adopting an Assumption-Based Argumentation Decision Support System - Efficient Decision Support Systems: Practice and Challenges from Current to Future - page 236

the theoretical reasoning. PARMENIDES 8 (Atkinson et al., 2006) is a software to structure the
debate over actions by adopting a particular argumentation scheme. GORGIAS 9 (Demetriou
& Kakas, 2003) implements an argumentation-based framework to support the decision
making of an agent within a modular architecture. Like the latter, our implementation,
called MARGO, incorporates abduction on missing information. Moreover, we can easily
extend it to compute the competing semantics since MARGO is built upon CaSAPI which is
an argumentation engine that implements the dispute derivations described in (Dung et al.,
2007).

6. Discussion
To our best knowledge, our argumentation-based mechanism for decision-making is the
only concrete argumentation system allowing concessions which is a crucial feature for
negotiations. Our framework is built upon assumption-based argumentation frameworks,
and provides mechanisms to evaluate decisions, to suggest decisions, and to interactively
explain in an intelligibleway the choice which has beenmade to make a certain decision, along
with the concessions, if any, made to support this choice. The underlying language in which
all the components of a decision problem are represented is a logic-based language, in which
preferences can be attached to goals. In our framework, arguments are defined by means
of tree-structures, thus facilitating their intelligibility. The concession-based mechanism is a
crucial feature of our framework required in different applications such as service selection
or agent-based negotiation. Our framework has been implemented and actually exploited in
different application domains, such as agent-based negotiation (Bromuri et al., 2009; Morge
& Mancarella, 2010), service-oriented agents (Guo et al., 2009), resource allocation (Morge
et al., 2009), computational model of trust (Matt et al., 2010) or embodied conversational
agents (Morge et al., 2010).
Our decision model only allows qualitative representation of goals. However, in many
practical applications, it is not natural to give a quantitative representation of goals. For
this purpose, it would be best to have a hybrid approach combining both quantitative and
qualitative aspects. Argumentation provides a natural framework for these hybrid systems
by providing a link between qualitative objectives and its quantitative representation.

7. Appendix A. Proofs
This appendix includes the proofs considered in this paper.

Proof 1 (Mapping between arguments) . Let
DF = DL

P I T P RV be a decision framework, G ∈G a set of goals and PABFS DF ( G ) , sm , , , , be

the set of PABFs associated with the goals G ⊇RV .

1. Let A be a structured argument concluding α ∈DL . The corresponding argument in some of the

A

( ) PAB F s ( d e n o t e d ) is defined in Definition 22.

DL and a : A α 2. Let us consider α an atomic formula in be an argument within one PABF in

PABFS DF ( ) L .

− 1

¯ Aisa

α ∈A α

{ α } ( A )= •Eth r sm DF . Therefore, is deduced by the singleton and

hypothetical argument defined such that:

8 http://cgi.csc.liv.ac.uk/~katie/Parmenides.html
9 http://www.cs.ucy.ac.cy/~nkd/gorgias/