Group polarization, the phenomenon where individuals become more extreme after interacting, has been gaining attention, especially with the rise of social media shaping people's opinions. Recent interest has emerged in formal reasoning about group polarization using logical systems. In this work we consider the modal logic PNL that captures the notion of agents agreeing or disagreeing on a given topic. Our contribution involves enhancing PNL with advanced formal reasoning techniques, instead of relying on axiomatic systems for analyzing group polarization. To achieve this, we introduce a semantic game tailored for (hybrid) extensions of PNL. This game fosters dynamic reasoning about concrete network models, aligning with our goal of strengthening PNL's effectiveness in studying group polarization. We show how this semantic game leads to a provability game by systemically exploring the truth in all models. This leads to the first cut-free sequent systems for some variants of PNL. Using polarization of formulas, the proposed calculi can be modularly adapted to consider different frame properties of the underlying model.

翻译：群体极化——个体在互动后观点趋于极端的现象——正日益受到关注，尤其是在社交媒体塑造人们意见的背景下。近年来，学界开始关注使用逻辑系统对群体极化进行形式化推理。本文研究模态逻辑PNL，该逻辑能够刻画主体在特定议题上赞同或反对的概念。我们的贡献在于运用先进的正式推理技术增强PNL，而非依赖公理系统来分析群体极化。为此，我们引入了一种专为PNL的（混合）扩展设计的语义博弈。该博弈促进了对具体网络模型的动态推理，与强化PNL在群体极化研究中效力的目标相一致。我们展示了如何通过系统探索所有模型中的真值，将这种语义博弈转化为可证性博弈，从而首次为PNL的若干变体建立了无切割的相继式系统。利用公式的极化性质，所提出的演算可模块化地适配，以考虑底层模型的不同框架属性。