加权加标网络的稳定与平衡

Stability and Balance in Many-Signed Networks

经典结构平衡理论对不带权重的加标网络有较为完善的研究。Morrissette(1958)将结构平衡理论推广到加权加标网络并加以经验研究。近年来出现了基于时态逻辑CTL的结构平衡逻辑研究,但所探讨的社会网络局限于不带权重的加标网络。本文将结构平衡逻辑推广到带权重的加标网络,引入几种适用的形式语言和语义,探讨由此得到的几个逻辑的表达能力,并给出证明系统。

The classical theory of structural balance provides an extensive study of 2-signed networks.Morrissette(1958)expanded this framework to encompass many-signed networks and applies it to empirical fields.Recent advancements in structural balance theory have incorporated temporal logic,specifically Computation Tree Logic(CTL).However,these studies have been limited to 2-signed networks.Our research extends this temporal approach to many-signed networks.We introduce formal languages and semantics tailored to this expanded framework,analyze the expressive power of the resulting logics,and develop axiomatizations for them.