We present an extension-based approach for computing and verifying preferences in an abstract argumentation system. Although numerous argumentation semantics have been developed previously for identifying acceptable sets of arguments from an argumentation framework, there is a lack of justification behind their acceptability based on implicit argument preferences. Preference-based argumentation frameworks allow one to determine what arguments are justified given a set of preferences. Our research considers the inverse of the standard reasoning problem, i.e., given an abstract argumentation framework and a set of justified arguments, we compute what the possible preferences over arguments are. Furthermore, there is a need to verify (i.e., assess) that the computed preferences would lead to the acceptable sets of arguments. This paper presents a novel approach and algorithm for exhaustively computing and enumerating all possible sets of preferences (restricted to three identified cases) for a conflict-free set of arguments in an abstract argumentation framework. We prove the soundness, completeness and termination of the algorithm. The research establishes that preferences are determined using an extension-based approach after the evaluation phase (acceptability of arguments) rather than stated beforehand. In this work, we focus our research study on grounded, preferred and stable semantics. We show that the complexity of computing sets of preferences is exponential in the number of arguments, and thus, describe an approximate approach and algorithm to compute the preferences. Furthermore, we present novel algorithms for verifying (i.e., assessing) the computed preferences. We provide details of the implementation of the algorithms (source code has been made available), various experiments performed to evaluate the algorithms and the analysis of the results.

翻译：我们提出了一种基于扩展的方法，用于在抽象论辩系统中计算和验证偏好。尽管先前已开发出众多论辩语义用于从论辩框架中识别可接受的论证集合，但基于隐含论证偏好的可接受性缺乏充分论证。基于偏好的论辩框架允许根据给定偏好确定哪些论证是合理的。本研究考虑了标准推理问题的逆问题，即在给定抽象论辩框架和一组已证成的论证后，计算论证上可能的偏好集。此外，还需要验证（即评估）计算出的偏好是否能导向可接受的论证集合。本文提出了一种新颖的方法和算法，用于穷举计算和枚举抽象论辩框架中无冲突论证集的所有可能偏好集（限定于三种已识别的情形）。我们证明了该算法的可靠性、完备性和终止性。研究表明，偏好在评估阶段（论证的可接受性）之后通过基于扩展的方法确定，而非事先声明。本研究重点探讨了基础语义、首选语义和稳定语义。我们证明，计算偏好集的复杂度随论证数量呈指数增长，因此描述了一种近似方法和算法用于计算偏好。此外，我们还提出了用于验证（即评估）计算所得偏好的新颖算法。我们提供了算法的实现细节（源代码已公开）、为评估算法而进行的各项实验以及结果分析。