[论文] When Stable and Preferred Semantics Agree: A Path-Based Approach

论文概要

研究领域: ML 作者: Yan Zhang, Kehan Liu 发布时间: 2026-10-24 arXiv: 2610.30176

中文摘要

本文研究抽象论辩框架中 preferred 与 stable 语义在何种结构条件下达成一致。方法基于攻击图中适当选取的路径集合及其诱导的二元关系：先建立一般性的路径判据，再实例化到若干路径类，得到以相应关系良基性表达的充分条件。所得条件严格推广了文献中两大结构性判据——Dung 的有限争议条件与 SCC 对称条件；特别地，取路径集为偶路径即可恢复 Dung 的经典结果。文中进一步引入两条无穷路径序列，各产生一族一致性条件：第一条序列由 Collapse 定理把无穷多良基性条件归约为三个本质不同的条件；第二条序列则产生无类似坍塌的、真正不同的条件。结果同时适用于有限与无限论辩框架，有限情形下表述可简化，并给出 stable 扩张存在的充分条件。

原文摘要

We investigate structural conditions under which preferred and stable semantics agree in abstract argumentation frameworks. Our approach is based on suitably chosen sets of paths in the attack graph and binary relations induced by them. We establish a general path-based criterion for semantic agreement and instantiate it with several classes of paths, obtaining sufficient conditions expressed in terms of well-foundedness of the corresponding relations. The resulting conditions strictly generalize two principal structural criteria for preferred and stable agreement in the literature: Dung's limited controversiality condition and the SCC-symmetry condition. In particular, Dung's result is recovered as a special case by taking the relevant path set to be the set of even paths. We further introduce two infinite sequences of path sets, each yielding a family of agreement conditions. For the first sequence, a Collapse Theorem reduces the infinitely many associated well-foundedness conditions to three essentially distinct ones, whereas the second sequence gives rise to genuinely distinct conditions with no analogous collapse. Our results apply to both finite and infinite argumentation frameworks, admit simplified formulations in the finite case, and also yield sufficient conditions for the existence of stable extensions.

---

*自动采集于 2026-10-24*

#论文 #arXiv #ML #小凯