We present a conceptualization providing an original domain-independent perspective on two crucial properties in reasoning: consistency and reinstatement. They emerge as a pair of dual characteristics, representing complementary requirements on the outcomes of reasoning processes. Central to our formalization are two underlying parametric relations: incompatibility and reinstatement violation. Different instances of these relations give rise to a spectrum of consistency and reinstatement scenarios. As a demonstration of versatility and expressive power of our approach we provide a characterization of various abstract argumentation semantics which are expressed as combinations of distinct consistency and reinstatement constraints. Moreover, we conduct an investigation into preserving these essential properties across different reasoning stages. Specifically, we delve into scenarios where a labelling is derived from other labellings through a synthesis function, using the synthesis of argument justification as an illustrative instance. We achieve a general characterization of consistency preservation synthesis functions, while we unveil an impossibility result concerning reinstatement preservation, leading us to explore an alternative notion to ensure feasibility. Our exploration reveals a weakness in the traditional definition of argument justification, for which we propose a refined version overcoming this limitation.

中文翻译：

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关于一致性和恢复的广义概念及其在形式论证中的保留


我们提出了一种概念化，为推理中的两个关键属性提供了原始的独立于领域的视角：一致性和恢复性。它们作为一对双重特征出现，代表了对推理过程结果的互补要求。我们形式化的核心是两个潜在的参数关系：不兼容性和恢复违规。这些关系的不同实例产生了一系列一致性和恢复场景。为了证明我们的方法的多功能性和表达能力，我们提供了各种抽象论证语义的表征，这些语义被表达为不同一致性和恢复约束的组合。此外，我们还进行了一项研究，以在不同的推理阶段保留这些基本属性。具体来说，我们深入研究通过综合函数从其他标签派生出标签的场景，并使用论证论证的综合作为说明性实例。我们实现了一致性保存综合函数的一般表征，同时我们揭示了有关恢复保存的不可能性结果，引导我们探索另一种概念以确保可行性。我们的探索揭示了论证论证的传统定义的弱点，为此我们提出了克服这一限制的改进版本。