🤖 AI Summary
This work addresses the challenge of formalizing multiscale causal relationships in complex systems by proposing a concise discrete hierarchical causal modeling framework. The framework introduces causal classes to abstract cross-level causal influences and integrates aggregation operators with discrete event-time mappings to characterize how high-level actors constrain, select, and organize the behaviors of low-level agents. The resulting formalism comprises three core components—causal classes, aggregation mechanisms, and temporal mappings—providing a unified and computationally tractable foundation for hierarchical causal analysis in complex systems.
📝 Abstract
We provide a brief primer for the idea behind formalising hierarchical causality in the context of complex systems. Here actors are not simply agents. Actors instantiate causation classes. Agents implement local dynamics in given levels or organisation in a given system. Hierarchical causality then describes how actor-level roles constrain, select, and organise agent-level behaviour across levels. The system then necessarily requires three additional structures. First, causation classes to abstract a given form of causal influence that an actor instantiates. Second, aggregation operators to move across the levels. Third, discrete event-time maps are required because the system comprises events, and the relation between local event counts and any global clock must be specified. Our formulation here is purposefully simple and discrete.