In this paper, we consider counting and projected model counting of extensions in abstract argumentation for various semantics. When asking for projected counts we are interested in counting the number of extensions of a given argumentation framework while multiple extensions that are identical when restricted to the projected arguments count as only one projected extension. We establish classical complexity results and parameterized complexity results when the problems are parameterized by treewidth of the undirected argumentation graph. To obtain upper bounds for counting projected extensions, we introduce novel algorithms that exploit small treewidth of the undirected argumentation graph of the input instance by dynamic programming (DP). Our algorithms run in time double or triple exponential in the treewidth depending on the considered semantics. Finally, we take the exponential time hypothesis (ETH) into account and establish lower bounds of bounded treewidth algorithms for counting extensions and projected extension.

本文探讨抽象论证中关于扩展项的计数和投影模型计数，提出了一种基于动态规划的新算法，并建立了经典和参数化的复杂度结果，考虑到评估参数化问题的树宽度，最后针对有界树宽算法建立下界，得出复杂度分析结论。

抽象论证推理的计数复杂度