Modal logics provide a versatile framework for reasoning about necessity and possibility, extending classical logic to capture a range of interpretations and applications. In epistemic logic, modalities may represent what agents know or believe, allowing for the formalization of concepts like common knowledge and belief dynamics in multi-agent systems.

On the other hand, group polarization and balance theory are fundamental concepts in understanding social dynamics, and their interplay with modal logic offers a novel perspective for analysis. In fact, one can model the evolution of opinions, preferences, or alliances using modalities such as knowledge, belief, and obligation. Combining these social theories with modal logic thus provides a rigorous and systematic approach to studying and predicting complex group behaviors.

In this talk, we will explore group polarization through dialogical game lenses. Games provide a powerful tool for bridging the gap between intended and formal semantics, often offering a conceptually natural approach to logic. We begin by examining the positive and negative modal logic (PNL) for giving formal reasoning about polarization. PNL models networks where agents can be related positively (they are “friends”) or negatively (they are “enemies”), but not both, and is used to axiomatize the class of networks that are balanced (to a certain degree). This is motivated by the study of group polarization, where the opinions or beliefs of individuals within a group become more extreme or polarized after interaction. We will first introduce a semantic game for PNL which enables dynamic reasoning over concrete network models, aligning with our overarching objective of enhancing PNL’s utility in understanding and analyzing group polarization. We will then show how the semantic game transitions naturally into a provability game, and how to extract proof systems out of them. We will finish the talk by giving an idea on how to view substructural calculi from a game semantic perspective, guided by intuitions about resource-conscious, and more specifically, cost-conscious reasoning. 

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