  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.
