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.

翻译：我们为复杂系统中形式化分层因果关系的概念提供了一个简明入门。在此，行动者（actors）并非仅仅是代理（agents）。行动者具现化因果关系类（causation classes），代理则在给定系统的特定组织层级中实现局部动力学。分层因果关系描述了行动者层级角色如何跨层级约束、选择和组织代理层级行为。系统因此必然需要三种额外结构：首先，因果关系类用于抽象行动者所具现的特定因果影响形式；其次，聚合算子（aggregation operators）用于实现层级间的转换；第三，需要离散事件-时间映射（discrete event-time maps），因为系统由事件构成，且必须指定局部事件计数与任何全局时钟之间的关系。我们的表述刻意保持简单离散。