Modelling qualitative uncertainty in formal argumentation is essential both for practical applications and theoretical understanding. Yet, most of the existing works focus on \textit{abstract} models for arguing with uncertainty. Following a recent trend in the literature, we tackle the open question of studying plausible instantiations of these abstract models. To do so, we ground the uncertainty of arguments in their components, structured within rules and premises. Our main technical contributions are: i) the introduction of a notion of expressivity that can handle abstract and structured formalisms, and ii) the presentation of both negative and positive expressivity results, comparing the expressivity of abstract and structured models of argumentation with uncertainty. These results affect incomplete abstract argumentation frameworks, and their extension with dependencies, on the abstract side, and ASPIC+, on the structured side.
翻译:在形式论辩中建模定性不确定性对于实际应用和理论理解均至关重要。然而,现有研究大多聚焦于处理不确定性的\textit{抽象}模型。遵循近期文献趋势,我们着手探讨这些抽象模型之合理实例化的开放性问题。为此,我们将论证的不确定性锚定于其构成要素——即结构化于规则与前提之中。我们的主要技术贡献包括:i) 提出一种能够同时处理抽象与结构化形式体系的表达力概念;ii) 通过呈现否定性与肯定性表达力结果,比较具有不确定性的抽象与结构化论辩模型的表达能力。这些结果涉及抽象层面的不完备抽象论辩框架及其依赖扩展,以及结构化层面的ASPIC+体系。