The classical theory of structural balance provides an extensive study of 2-signed networks.Morrissette(1958)expanded this framework to encompass many-signed net-works 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 tai-lored to this expanded framework,analyze the expressive power of the resulting logics,and develop axiomatizations for them.
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