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Recently, an opinion dynamics model has been proposed to describe a networkof individuals discussing a set of logically interdependent topics. For eachindividual, the set of topics and the logical interdependencies between thetopics (captured by a logic matrix) form a belief system. We investigate therole the logic matrix and its structure plays in determining the finalopinions, including existence of the limiting opinions, of a strongly connectednetwork of individuals. We provide a set of results that, given a set ofindividuals' belief systems, allow a systematic determination of which topicswill reach a consensus, and which topics will disagreement in arise. Forirreducible logic matrices, each topic reaches a consensus. For reducible logicmatrices, which indicates a cascade interdependence relationship, conditionsare given on whether a topic will reach a consensus or not. It turns out thatheterogeneity among the individuals' logic matrices, including especiallydifferences in the signs of the off-diagonal entries, can be a key determiningfactor. This paper thus attributes, for the first time, a strong diversity oflimiting opinions to heterogeneity of belief systems in influence networks, inaddition to the more typical explanation that strong diversity arises fromindividual stubbornness.

Consensus and Disagreement of Heterogeneous Belief Systems in Influence Networks