Reasoning with probabilistic information has recently attracted considerable attention in argumentation, and formalisms of Probabilistic Abstract Argumentation (PAA), Probabilistic Bipolar Argumentation (PBA) and Probabilistic Structured Argumentation (PSA) have been proposed. These foundational advances have been complemented with investigations on the complexity of some approaches to PAA and PBA, but not to PSA. We study the complexity of an existing form of PSA, namely Probabilistic Assumption-Based Argumentation (PABA), a powerful, implemented formalism which subsumes several forms of PAA and other forms of PSA. Specifically, we establish membership (general upper bounds) and completeness (instantiated lower bounds) of reasoning in PABA for the class ${\mathsf{FP}}^{\mathrm{\#}\mathsf{P}}$ (of functions with a $\mathrm{\#}\mathsf{P}$-oracle for counting the solutions of an $\mathsf{NP}$ problem) with respect to newly introduced probabilistic verification, credulous and sceptical acceptance function problems under several ABA semantics. As a by-product necessary to establish PABA complexity results, we provide a comprehensive picture of the ABA complexity landscape (for both flat and generic, possibly non-flat ABA) for the classical decision problems of verification, existence, credulous and sceptical acceptance under those ABA semantics.

最近，关于概率信息的推理在争论中引起了相当大的关注，并且提出了概率抽象论证（PAA），概率双极论证（PBA）和概率结构论证（PSA）的形式主义。这些基础性的进步已经得到了对某些针对PAA和PBA而非PSA的方法的复杂性的研究的补充。我们研究了PSA现有形式的复杂性，即基于概率假设的论证（PABA），它是一种强大的，已实现的形式主义，其中包含了几种形式的PAA和其他形式的PSA。具体来说，我们针对该类在PABA中建立推理的隶属度（一般上限）和推理的完整性（实例化下限）${\mathsf{FP}}^{\mathrm{＃}\mathsf{P}}$ （具有 $\mathrm{＃}\mathsf{P}$-oracle用于计算解决方案 $\mathsf{NP}$问题）有关新引入的概率验证，几种ABA语义下的怀疑和怀疑的接受函数问题。作为建立PABA复杂度结果所必需的副产品，我们提供了ABA复杂度态势的全面描述（适用于扁平和通用，可能是非扁平ABA），用于经典决策问题下的验证，存在，可信和怀疑接受这些ABA语义。