逻辑约束下信念系统动力学的图论分析
Graph-Theoretic Analysis of Belief System Dynamics under Logic Constraints
摘要：
观点的形成不能仅仅被建模为一套原则的意识形态演绎;相反，重复的社会互动和陈述之间的逻辑约束在信念体系的构建中是重要的。我们解决三个基本问题，在社会舆论动态分析：（一）将一个信念系统收敛？(ii)需要多长时间才能收敛？(iii)它在哪里汇合？我们提供了图论的答案，这些问题的一个模型的意见动态的信仰系统与逻辑约束。我们的研究结果表明，信仰系统的收敛特性对底层社会网络和一组逻辑约束（这些约束将信仰与不同陈述联系起来）的隐含依赖性。此外，我们提供了一个明确的分析各种常用的大规模网络模型。
英文摘要：
Opinion formation cannot be modeled solely as an ideological deduction from a set of principles; rather, repeated social interactions and logic constraints among statements are consequential in the construct of belief systems. We address three basic questions in the analysis of social opinion dynamics: (i) Will a belief system converge? (ii) How long does it take to converge? (iii) Where does it converge? We provide graph-theoretic answers to these questions for a model of opinion dynamics of a belief system with logic constraints. Our results make plain the implicit dependence of the convergence properties of a belief system on the underlying social network and on the set of logic constraints that relate beliefs on different statements. Moreover, we provide an explicit analysis of a variety of commonly used large-scale network models.
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