Modeling Logical Interdependencies: Quantifying Systemic Risk From Rule-Governed Actions

Systemic risk in critical infrastructure is often analyzed through physical, geographic, and cyber interdependencies. Yet infrastructures are also interdependent through the governing rules that organize human action. These rule-mediated connections are a form of logical interdependency, and breakdowns in rule-governed action can create pathways through which disruption spreads. This paper develops a framework for diagnosing and quantifying this underrecognized source of systemic risk. It does so by modeling logical interdependencies as rule-mediated control relations that shape whether interconnected infrastructures remain within safe operating bounds or drift toward failure. Integrating Institutional Grammar, STAMP, and Bayesian inference, the framework translates governing rules into structured control relations, represents them within a socio-technical control architecture, and quantifies how failures in those relations propagate across interconnected infrastructures. We demonstrate the framework through a reservoir system case study centered on Lake Mendocino, California, where safety depends not only on reservoir infrastructure and hydrologic conditions, but also on distributed authority, communication requirements, and operational protocols. The results show that logical interdependencies make non-trivial contributions to modeled systemic risk, with baseline probabilities of 7% for Coyote Valley Dam failure and 3% for downstream community impacts under the modeled conditions. More importantly, the analysis reveals hidden logical risk: rules and control relations that appear routine in normal operation yet become disproportionately important when the Bayesian model traces which factors most strongly contribute to a failure scenario. The paper moves logical interdependencies from a residual conceptual category to a systematically identifiable and quantitatively analyzable pathway of systemic risk.