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Unified Opinion Dynamic Modeling as Concurrent Set Relations in Rewriting Logic

Carlos Olarte, Carlos Ramírez, Camilo Rocha, Frank Valencia

TL;DR

This paper introduces a unified framework for dynamic opinion models on social networks using concurrent set relations. It encodes agent interactions as influence graphs and combines an atomic update relation with a strategy to capture synchronous, asynchronous, and parallel updates, implemented as a fully executable Maude rewrite theory. Three models—DeGroot, gossip-based, and a hybrid variant—are shown as instances of the framework, enabling formal analysis, reachability, and probabilistic model checking to study consensus and polarization. The approach provides a formal, extensible platform for exploring social phenomena with concurrency tools, while acknowledging state explosion and outlining future directions for probabilistic extensions and real-world validation.

Abstract

Social media platforms have played a key role in weaponizing the polarization of social, political, and democratic processes. This is, mainly, because they are a medium for opinion formation. Opinion dynamic models are a tool for understanding the role of specific social factors on the acceptance/rejection of opinions because they can be used to analyze certain assumptions on human behaviors. This work presents a framework that uses concurrent set relations as the formal basis to specify, simulate, and analyze social interaction systems with dynamic opinion models. Standard models for social learning are obtained as particular instances of the proposed framework. It has been implemented in the Maude system as a fully executable rewrite theory that can be used to better understand how opinions of a system of agents can be shaped. This paper also reports an initial exploration in Maude on the use of reachability analysis, probabilistic simulation, and statistical model checking of important properties related to opinion dynamic models.

Unified Opinion Dynamic Modeling as Concurrent Set Relations in Rewriting Logic

TL;DR

This paper introduces a unified framework for dynamic opinion models on social networks using concurrent set relations. It encodes agent interactions as influence graphs and combines an atomic update relation with a strategy to capture synchronous, asynchronous, and parallel updates, implemented as a fully executable Maude rewrite theory. Three models—DeGroot, gossip-based, and a hybrid variant—are shown as instances of the framework, enabling formal analysis, reachability, and probabilistic model checking to study consensus and polarization. The approach provides a formal, extensible platform for exploring social phenomena with concurrency tools, while acknowledging state explosion and outlining future directions for probabilistic extensions and real-world validation.

Abstract

Social media platforms have played a key role in weaponizing the polarization of social, political, and democratic processes. This is, mainly, because they are a medium for opinion formation. Opinion dynamic models are a tool for understanding the role of specific social factors on the acceptance/rejection of opinions because they can be used to analyze certain assumptions on human behaviors. This work presents a framework that uses concurrent set relations as the formal basis to specify, simulate, and analyze social interaction systems with dynamic opinion models. Standard models for social learning are obtained as particular instances of the proposed framework. It has been implemented in the Maude system as a fully executable rewrite theory that can be used to better understand how opinions of a system of agents can be shaped. This paper also reports an initial exploration in Maude on the use of reachability analysis, probabilistic simulation, and statistical model checking of important properties related to opinion dynamic models.
Paper Structure (18 sections, 2 theorems, 17 equations, 1 figure)

This paper contains 18 sections, 2 theorems, 17 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Organization.
  3. Overview of Rewriting Logic and Maude
  4. Meta-programming.
  5. Set Relations
  6. Vaccine Example.
  7. Opinion Dynamic Models
  8. The Atomic Relation
  9. Gossip-based Models
  10. De Groot
  11. The Hybrid Model
  12. The Framework in Rewriting Logic
  13. Influences, Opinions, and State
  14. Strategies and the Atomic Relation
  15. Experimentation
  16. ...and 3 more sections

Key Result

theorem 1

${\REL_\text{DeGroot}} \subseteq {\REL_\text{hybrid}}$.

Figures (1)

  • Figure 1: Graph representing opinion and influence interaction in a social system. Initial opinions are given within the box below each node. The labels on each edge $(u,v)$ represent the influence value of agent $u$ over agent $v$.

Theorems & Definitions (11)

  • definition 1: Asynchronous Set Relation
  • definition 2: Parallel Set Relation
  • definition 3: $\REL$-strategy
  • definition 4: Synchronous Relation
  • definition 5
  • definition 6
  • definition 7
  • theorem 1
  • proof
  • theorem 2
  • ...and 1 more