Reasoning About Group Polarization: From Semantic Games to Sequent Systems

TL;DR

This paper develops a semantic game approach for a modal logic PNL to analyze group polarization, resulting in new sequent systems that improve formal reasoning about social opinion dynamics.

Contribution

It introduces a semantic game for PNL, leading to the first cut-free sequent systems and enabling modular analysis of group polarization.

Findings

Semantic game enhances reasoning about group polarization.

First cut-free sequent systems for PNL variants.

Modular calculus adapts to different model properties.

Abstract

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.