Abstract argumentation frameworks (AFs), originally proposed by Dung, constitute a central formal model for the study of computational aspects of argumentation in AI. Credulous and skeptical acceptance of arguments in a given AF are well-studied problems both in terms of theoretical analysis—especially computational complexity—and the development of practical decision procedures for the problems. However, AFs make the assumption that all attacks between arguments are certain (i.e., present attacks are known to exist, and missing attacks are known to not exist), which can in various settings be a restrictive assumption. A generalization of AFs to incomplete AFs was recently proposed as a formalism that allows the representation of both uncertain attacks and uncertain arguments in AFs. In this article, we explore the impact of allowing for modeling such uncertainties in AFs on the computational complexity of natural generalizations of acceptance problems to incomplete AFs under various central AF semantics. Complementing the complexity-theoretic analysis, we also develop the first practical decision procedures for all of the NP-hard variants of acceptance in incomplete AFs. In terms of complexity analysis, we establish a full complexity landscape, showing that depending on the variant of acceptance and property/semantics, the complexity of acceptance in incomplete AFs ranges from polynomial-time decidable to completeness for ${\mathrm{\Sigma }}_3^p$. In terms of algorithms, we show through an extensive empirical evaluation that an implementation of the proposed decision procedures, based on boolean satisfiability (SAT) solving, is effective in deciding variants of acceptance under uncertainties. We also establish conditions for what type of atomic changes are guaranteed to be redundant from the perspective of preserving extensions of completions of incomplete AFs, and show that the results allow for considerably improving the empirical efficiency of the proposed SAT-based counterexample-guided abstraction refinement algorithms for acceptance in incomplete AFs for problem variants with complexity beyond NP.

Dung最初提出的抽象论证框架（AFs）构成了研究AI中论证的计算方面的中央形式模型。从理论分析（尤其是计算复杂性）以及针对问题的实际决策程序的发展来看，对给定AF中的论点的怀疑和怀疑性接受都是经过充分研究的问题。但是，AF假设参数之间的所有攻击都是确定的（即，已知存在当前攻击，并且已知不存在丢失的攻击），在各种情况下，这可能是限制性的假设。最近提出了将AF泛化为不完整的AF的形式化，可以表示AF中不确定的攻击和不确定的论点。在本文中，我们探讨了允许在AF中对此类不确定性进行建模对各种中央AF语义下的接受问题到不完全AF的自然概括的计算复杂度的影响。作为复杂性理论分析的补充，我们还为不完全AF中接受的所有NP硬变体开发了第一个实际的决策程序。在复杂度分析方面，我们建立了一个完整的复杂度格局，表明根据接受和属性/语义的变体，不完整AF中接受的复杂度范围从可确定的多项式时间到完整性的范围。我们还为不完全AF中接受的所有NP-hard变体开发了第一个实际的决策程序。在复杂度分析方面，我们建立了一个完整的复杂度格局，表明根据接受和属性/语义的变体，不完整AF中接受的复杂度范围从可确定的多项式时间到完整性的范围。我们还为不完全AF中接受的所有NP-hard变体开发了第一个实际的决策程序。在复杂度分析方面，我们建立了一个完整的复杂度格局，表明根据接受和属性/语义的变体，不完整AF中接受的复杂度范围从可确定的多项式时间到完整性的范围。${\mathrm{\Sigma }}_3^p$。在算法方面，我们通过广泛的经验评估表明，基于布尔可满足性（SAT）解决方案的拟议决策程序的实现可有效地确定不确定性下的接受变量。从保留不完整AF的完成扩展的角度来看，我们还建立了确保什么类型的原子变化是冗余的条件，并表明结果可大大提高建议的基于SAT的反例指导的抽象提炼的经验效率复杂度超出NP的问题变体在不完全AF中接受的算法。