The knowledge representation of a decision-maker in control of a complex system can be structured in several levels of abstraction in a functional hierarchy. The role of such an abstraction hierarchy in supervisory systems control is reviewed, and the difference between causal and intentional systems and formal games is discussed in terms of the role of an abstraction hierarchy in the related decision strategies. This relationship is then discussed with reference to the classical psychological problem-solving research of O. Selz (1922) and others. Finally, the implications for the design of decision-support systems are discussed. It is argued that an explicit description of the functional properties of the system to be controlled in terms of an abstraction hierarchy is necessary for a consistent design of databases and display formats for decision-support systems. Also, it is necessary to consider the role of the abstraction hierarchy in reasoning when planning experiments on human decision-making.