Bipolarity in Argumentation Graphs: Towards a Better Understanding

Abstract

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. Any correspondance concerning this service should be sent to the repository administrator: staff-oatao@listes-diff.inp-toulouse.fr Bipolarity in argumentation graphs: Towards a better understanding Claudette Cayrol, Marie-Christine Lagasquie-Schiex * IRIT-UPS, Université de Toulouse, FranceA B S T R A C T Different abstract argumentation frameworks have been used for various applications within multi-agents systems. Among them, bipolar frameworks make use of both attack and support relations between arguments. However, there is no single interpretation of the support, and the handling of bipolarity cannot avoid a deeper analysis of the notion of support.In this paper we consider three recent proposals for specializing the support relation in abstract argumentation: the deductive support, the necessary support and the evidential support. These proposals have been developed independently within different frameworks. We restate these proposals in a common setting, which enables us to undertake a comparative study of the modellings obtained for the three variants of the support. We highlight relationships and differences between these variants, namely a kind of duality between the deductive and the necessary interpretations of the support.

Probabilistic abstract argumentation: an investigation with Boltzmann machines

“…Hence, this argumentation graph is not meant to account for dependence arcs as commonly understood in graphical models, and to capture the dependences, one may draw a Markov network as given in Figure 7, or a factor graph as in Figure 8.This example may be considered in a modified setting for abstract argumentation with some support relations (see e.g. Cayrol and Lagasquie-Schiex, 2013), so that arguments B and C are related by some support relations, specifying so some probabilistic dependences. In this view, we might induce a Markov network from an argumentation graph to capture the probabilistic dependences among the labels of arguments, but this matter is not addressed in this paper.…”

Generalizations of Dung Frameworks and Their Role in Formal Argumentation

“…In particular, the ability to model various notions of support appears useful. This observation has led to the development of so-called bipolar argumentation frameworks [27,28] where both of the relations are modeled.…”

“…The combination of attack and support leads to indirect attacks, referred to as complex attacks in [28]. For instance, there is a supported attack from a 1 to b if there is a sequence of support links from a 1 to a n and an attack from a n to b.…”

“…In [28] an analysis of three different types of support is carried out: deductive support, necessary support and evidential support. The former two are quite strong notions and, as shown in that paper, dual to each other.…”

“…This can make modeling e.g. collective [52] or supportive [28] relations unpleasant if not problematic.…”