Formal Reasoning About Group Polarization: From Semantic Games to Sequent Calculi

핵심 개념

This work introduces a semantic game and a provability game for reasoning about group polarization using the modal logic PNL. The games lead to the development of cut-free sequent calculi for PNL and its extensions, which can be used for automated reasoning about social network dynamics and polarization.

초록

The paper focuses on formal reasoning about group polarization, where individuals become more extreme in their opinions after interacting within a group. The authors use the modal logic PNL, which captures the notion of agents agreeing or disagreeing on a given topic, as the basis for their work.
The key contributions are:

Introducing a semantic game that characterizes truth in a given PNL model. This game provides an alternative to the standard Kripke semantics and supports dynamic reasoning about concrete network models.

Defining a disjunctive provability game that lifts the semantic game to logical validity. This game is shown to be adequate with respect to the logic, in the sense that the existence of winning strategies for the proponent corresponds to logical validity.

Developing cut-free sequent calculi DS and DScc for PNL and its extension to collectively connected models, respectively. These proof systems are derived from the structure of the provability game and provide a foundation for automated reasoning about group polarization.

Showing how the global and local link change modalities from previous work can be incorporated into the proposed framework, enabling the analysis of dynamic social network models.

The authors demonstrate the expressiveness of their approach through examples, and mention a prototypical implementation using rewriting logic and Maude.

통계

None.

인용구

None.

핵심 통찰 요약

Reasoning About Group Polarization: From Semantic Games to Sequent Systems

by Robe... 게시일 arxiv.org 05-03-2024

https://arxiv.org/pdf/2405.01322.pdf

더 깊은 질문

How can the proposed framework be extended to capture other important properties of social networks, such as the formation of echo chambers or the emergence of extremist views

The proposed framework can be extended to capture other important properties of social networks by introducing additional modalities and rules in the proof system. For instance, to model the formation of echo chambers, where individuals are only exposed to information that aligns with their existing beliefs, new modalities can be introduced to represent this behavior. By incorporating rules that govern how information is shared and received within the network, the proof system can be adapted to analyze the formation and reinforcement of echo chambers. Similarly, to model the emergence of extremist views, modalities that capture radicalization processes and rules that govern the spread of extreme ideologies can be integrated into the framework. By extending the framework with these additional features, it becomes more versatile in capturing a wider range of social network dynamics related to group polarization.

What are the computational complexity implications of the developed proof systems, and how can they be optimized for practical applications

The computational complexity implications of the developed proof systems depend on the size of the network model and the complexity of the logical formulas being analyzed. As the proof systems involve game semantics and sequent calculus, the complexity can vary based on the number of agents, the structure of the network, and the depth of reasoning required. To optimize the proof systems for practical applications, techniques such as parallelization, heuristic search algorithms, and efficient data structures can be employed. By leveraging these optimization strategies, the computational efficiency of the proof systems can be enhanced, making them more suitable for real-world applications with large-scale social network models and complex logical reasoning tasks.

Can the games and proof systems be adapted to reason about group polarization in the context of other logical formalisms, such as epistemic or temporal logics

The games and proof systems developed for reasoning about group polarization can be adapted to other logical formalisms, such as epistemic or temporal logics, by modifying the rules and modalities to align with the specific requirements of the new formalism. For epistemic logics, the framework can be extended to incorporate knowledge-sharing dynamics, belief updates, and information propagation rules within the social network. Similarly, for temporal logics, the framework can be adjusted to capture the evolution of beliefs and opinions over time, considering temporal constraints and dependencies in the reasoning process. By adapting the games and proof systems to different logical formalisms, the framework can be applied to a broader range of scenarios and provide insights into group polarization dynamics in various contexts.