Argumentation - justification, localization and propagation of admissibility

Abstract argumentation frameworks are used to study various aspects of interaction between arguments. One most fundamental such interaction is that some arguments may attack some other arguments. In a sense, only those arguments finally matter that are successfully defended against the attackers. Such arguments are called admissible. This thesis incorporates three papers in this area of research, two of which are devoted to the admissibility of arguments. The first paper introduces the notion of the admissibility backing of an argument – a minimal set of admissible arguments that can successfully defend (respectively attack) a given argument against its attackers (defenders). This paper shows how admissible backings can help us localize the admissibility of an argument. It does so by separating those arguments that are relevant to the admissibility of a given argument from those that are not. Independent corroboration for this approach is provided by showing how major results in Dung’s approach to argumentation can be obtained using admissibility backings. The second paper explores the propagation of admissibility backings in the following sense: under what condition, and in what way, an admissibility backing of a given argument will contribute to the backing of a different argument? It is shown that under certain conditions, the propagation is transitive. It is further shown how the propagation of admissibility backings can be used to partition an argumentation framework to independent sub-frameworks. This is indicative of an interesting approach to the splitting and merging of different argumentation frameworks, a theoretical investigation of which is left for future research. The last paper explores a novel approach to marrying the argumentation frameworks to defeasible reasoning. The desired goal behind this approach is that an argument that is deemed justied in an argumentation framework should indeed satisfy our expectations as per defeasible reasoning. The efficacy of this approach is shown by providing a mapping from it to Dung’s argumentation framework.