Dealing with controversial information is an important issue in several application contexts. Formal argumentation enables reasoning on arguments for and against a claim to decide on an outcome. Dung's abstract Argumentation Framework (AF) has emerged as a central formalism in argument-based reasoning. Key aspects of the success and popularity of Dung's framework include its simplicity and expressiveness. Integrity constraints help to express domain knowledge in a compact and natural way, thus keeping easy the modeling task even for problems that otherwise would be hard to encode within an AF. In this paper, we first explore two intuitive semantics based on Kleene and Lukasiewicz logics, respectively, for AF augmented with (strong) constraints—the resulting argumentation framework is called Constrained AF (CAF). Then, we propose a new argumentation framework called Weak constrained AF (WAF) that enhances CAF with weak constraints. Intuitively, these constraints can be used to find “optimal” solutions to problems defined through CAF. We provide a detailed complexity analysis of CAF and WAF, showing that strong constraints do not increase the expressive power of AF in most cases, while weak constraints systematically increase the expressive power of CAF (and AF) under several well-known argumentation semantics.

中文翻译：

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具有强约束和弱约束的抽象论证框架


在多个应用程序环境中，处理有争议的信息是一个重要问题。正式论证可以对支持和反对某个主张的论点进行推理，从而决定结果。邓的抽象论证框架（AF）已成为基于论证的推理的核心形式主义。 Dung 框架的成功和流行的关键在于其简单性和表现力。完整性约束有助于以紧凑、自然的方式表达领域知识，从而使建模任务变得简单，即使对于难以在 AF 中编码的问题也是如此。在本文中，我们首先分别探索基于 Kleene 和 Lukasiewicz 逻辑的两种直观语义，用于增强（强）约束的 AF——由此产生的论证框架称为约束 AF (CAF)。然后，我们提出了一种称为弱约束 AF (WAF) 的新论证框架，它增强了弱约束下的 CAF。直观上，这些约束可用于找到通过 CAF 定义的问题的“最佳”解决方案。我们对 CAF 和 WAF 进行了详细的复杂性分析，表明在大多数情况下强约束不会增加 AF 的表达能力，而弱约束在几种众所周知的论证语义下系统地增加了 CAF（和 AF）的表达能力。