Modularity is a central principle throughout the design process for cyber-physical systems. Modularity reduces complexity and increases reuse of behavior. In this paper we pose and answer the following question: how can we identify independent modules' within the structure of reactive control architectures? To this end, we propose a graph-structured control architecture we call a decision structure, and show how it generalises some reactive control architectures which are popular in Artificial Intelligence (AI) and robotics, specifically Teleo-Reactive programs (TRs), Decision Trees (DTs), Behavior Trees (BTs) and Generalised Behavior Trees (k-BTs). Inspired by the definition of a module in graph theory, we define modules in decision structures and show how each decision structure possesses a canonical decomposition into its modules.