Reasoning with defeasible and conflicting knowledge in an argumentative form is a key research field in computational argumentation. Reasoning under various forms of uncertainty is both a key feature and a challenging barrier for automated argumentative reasoning. It was shown that argumentative reasoning using probabilities faces in general high computational complexity, in particular for the so-called constellation approach. In this paper, we develop an algorithmic approach to overcome this obstacle. We refine existing complexity results and show that two main reasoning tasks, that of computing the probability of a given set being an extension and an argument being acceptable, diverge in their complexity: the former is #P-complete and the latter is #-dot-NP-complete when considering their underlying counting problems. We present an algorithm for the complex task of computing the probability of a set of arguments being a complete extension by using dynamic programming operating on tree-decompositions. An experimental evaluation shows promise of our approach.

在计算论证中，推理具有不可靠和冲突的知识是一个重要的研究领域。本文提出了一种算法方法来克服概率论证在推理任务中所面临的高计算复杂性难题，并通过动态规划算法在树分解上操作，实现了对一组给定的论证是否是完整扩展的概率进行计算。实验结果显示了该方法的潜力。

推进基于星座方法的概率论辩算法