# WP1

** Defining Richer Argumentation Systems **

**Aim**

The aim of this WP is to define a new generation of argumentation systems that underpin the services that are emerging as core functions of multiparty argumentation. These include generation and evaluation of arguments, and selection of arguments to put forward. For this purpose, we will develop an axiomatic approach where axioms are the desirable properties that the new systems should satisfy.

**Background**

In [Dung95], deliberation is somewhat “simplistic”, as it classifies arguments into two categories only: acceptable and unacceptable arguments. Several works, (e.g., [BH01,CL05,MT08]) have considered and explored the possibility of discriminating between arguments using a larger number of categories or continuous numerical scales. Under this approach, the argumentation process is divided into two steps: a valuation of the relative strength of the arguments, and then the selection of the most acceptable ones. In the valuation step, it is usual to distinguish two different types of valuations: intrinsic valuation, where the value of an argument is independent of its interactions with the other arguments (e.g.,[Pollock92,PS97]); interaction-based valuation, where the value of an argument depends on its attackers [BH01,CL05]. Recently [MT08] have proposed a measure of strength of arguments using the paradigm of non-cooperative game theory.

**Challenges/Subtasks**

**1. Classification of arguments**

coalitions of arguments and the respective attack/defence branches are considered. First, a coalitional game (see e.g. [Owen95]) representing the relevant information about attacks and defences to arguments inside (or outside) coalitions of arguments, is constructed. Second, power indices [SS54,Owen95,MP08] may be used to convert the information about the strength of attacks and defences of coalitions of arguments into a single valuation of each argument. We plan to compare the different assumptions made in our approach to support the use of power indices for arguments valuation by means of an axiomatic approach. E.g., one intuitive property that an argument valuation should satisfy is that the dialectical properties of admissibility and stability should confer more strength to an argument in a dispute. As was observed in [MT08], the measures of [BH01,CL05] do not satisfy in general this property

**2. Classification of attacks**

interpretation of weights is demanded, and the authors suggest a possible interpretation of weights in a multi agent setting in terms of the number of votes that support the attack. However, as it is well known from the theory of voting systems, the number of votes does not necessarily represent the importance of an attack. In addition, the configurations of links associated to an abstract argumentation framework provide information about which multiple attacks are feasible, and this information should be considered in the computation of the strength of attacks. In order to integrate the information about the votes of agents with the information about the restriction on the feasibility of multiple attacks provided by an abstract argumentation framework, we may make use of coalitional games with restriction in cooperation [BOT92].

**3. Revision of an argumentation system**

Inspired by monotonicity results for solutions in coalitional games [Sprumont90, Moretti08], it will be interesting to investigate monotonicity properties of a valuation method when new elements are added to an argumentation system. E.g., it would be counter-intuitive to define revision operations based on valuation that allocate less (more) strength to an argument when some of the attacks directed to such an argument are removed (added).