Argumentation problems are concerned with determining the acceptability of a set of arguments from their relational structure. When the available information is uncertain, probabilistic argumentation frameworks provide modelling tools to account for it. The first contribution of this paper is a novel interpretation of probabilistic argumentation frameworks as probabilistic logic programs. Probabilistic logic programs are logic programs in which some of the facts are annotated with probabilities. We show that the programs representing probabilistic argumentation frameworks do not satisfy a common assumption in probabilistic logic programming (PLP) semantics, which is, that probabilistic facts fully capture the uncertainty in the domain under investigation. The second contribution of this paper is then a novel PLP semantics for programs where a choice of probabilistic facts does not uniquely determine the truth assignment of the logical atoms. The third contribution of this paper is the implementation of a PLP system supporting this semantics: smProbLog. smProbLog is a novel PLP framework based on the probabilistic logic programming language ProbLog. smProbLog supports many inference and learning tasks typical of PLP, which, together with our first contribution, provide novel reasoning tools for probabilistic argumentation. We evaluate our approach with experiments analyzing the computational cost of the proposed algorithms and their application to a dataset of argumentation problems.

翻译：论证问题关注的是如何根据论据之间的关系结构确定一组论据的可接受性。当可用信息存在不确定性时，概率论证框架提供了建模工具来应对这一问题。本文的第一个贡献在于，提出了一种将概率论证框架解释为概率逻辑程序的新方法。概率逻辑程序是一类逻辑程序，其中部分事实被标注了概率值。我们证明，表示概率论证框架的程序并不满足概率逻辑编程语义中的一项常见假设，即概率事实完全捕获了研究领域中的不确定性。本文的第二个贡献，则是针对那些概率事实的选择无法唯一确定逻辑原子真值赋值的程序，提出了一种新颖的概率逻辑编程语义。本文的第三个贡献是实现了一个支持该语义的概率逻辑编程系统：smProbLog。smProbLog是基于概率逻辑编程语言ProbLog的新型概率逻辑编程框架。该系统支持概率逻辑编程中典型的多种推理与学习任务，结合我们的第一个贡献，为概率论证提供了新颖的推理工具。我们通过实验分析了所提算法的计算成本及其在论证问题数据集上的应用，对提出的方法进行了评估。