Lighthouse Principle for Diffusion in Social Networks

TL;DR

This paper introduces a logical framework to analyze influence relations in social networks, providing formal tools to understand how influence propagates based on network structure.

Contribution

It presents a novel logical system combining Armstrong axioms and a Lighthouse axiom to characterize influence relations in social networks with proven soundness, completeness, and decidability.

Findings

The logical system accurately captures influence relations in threshold social network models.

The system is proven to be sound, complete, and decidable.

It extends existing models with a new axiom for influence analysis.

Abstract

The article investigates influence relation between two sets of agents in a social network. It proposes a logical system that captures propositional properties of this relation valid in all threshold models of social networks with the same topological structure. The logical system consists of Armstrong axioms for functional dependence and an additional Lighthouse axiom. The main results are soundness, completeness, and decidability theorems for this logical system.