# Graph-Theoretic Analysis of Belief System Dynamics under Logic Constraints

arXiv: https://arxiv.org/abs/1810.02456 · HTML: https://mlsanity.com/paper/1810.02456/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Oct 2018.

## Built on by (most cited first, 3 of 3)

- [Communication-efficient Distributed Cooperative Learning with Compressed Beliefs](https://mlsanity.com/paper/2102.07767/) (2021)
- [Scalable Average Consensus with Compressed Communications](https://mlsanity.com/paper/2109.06996/) (2021)
- [Matrix-weighted networks for modeling multidimensional dynamics](https://mlsanity.com/paper/2410.05188/) (2024)

## Abstract (arXiv)

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.