Arguing with Doubt
Michael A. Müller

Abstract:
There is little agreement in formal argumentation on how to evaluate bipolar argumentation, where supporting arguments are considered in addition to attacking arguments. In contrast, informal argumentation has well established approaches to argumentation that deal with supports. In this thesis, we provide a new approach to bipolar argumentation that incorporates two features of informal argumentation: arguments have structure and one is allowed to doubt unattacked arguments. For that purpose, we define structured bipolar argumentation frameworks (SBAFs), which differ from bipolar argumentation frameworks by having structured arguments and from structured argumentation by having an explicit support relation. We provide two types of extension-based semantics for SBAFs: one that gives argument extensions and one that gives language extensions, where the latter are sets of sentences instead of arguments. We show that what we call coherent argument extensions and adequate language extensions correspond under certain assumptions. We further show how preferred semantics can be retrieved from weakly coherent argument extensions and how deductive support can be retrieved from strongly coherent argument extensions. We additionally provide a brief principled comparison of weakly and strongly coherent argument extensions and show that they are distinguished by the principle “directionality”. Finally, we indicate how a form of knowledge-based reasoning can be implemented in SBAFs by distinguishing between doubtable and contestable sentences, where the latter have to be accepted in absence of attacks.