Generalized dynamic stock and flow systems: An AI approach Action editor: Cleotilde Gonzalez Marco Ragni ⇑ , Felix Steffenhagen, Andreas Klein Center for Cognitive Science, University of Freiburg, Friedrichstr. 50, D-79098 Freiburg, Germany Received 6 May 2010; received in revised form 31 October 2010; accepted 4 November 2010 Available online 6 January 2011 Abstract A well-known problem in complex cognition is the so-called dynamic stocks and flows task (DSF). The challenge in this task is to control different flows, e.g. the inflows and outflows of water to a tank, towards a specified goal configuration, i.e. a certain amount of water in the tank. The problem is that some flows are exogenously controlled with a hidden dynamic. These flows need to be coun- terbalanced by setting endogenous flows. Since the dynamic underlying the hidden flows can be any computable function, this task can be classified as computationally complex. Psychological findings show that humans have difficulties in dealing with such dynamic systems. In this article, we present a formal generalization of this task and present a computational approach for solving such tasks as a first step towards an assistance system for complex system control. Ó 2011 Elsevier B.V. All rights reserved. Keywords: Complex cognition; Dynamic stock and flow systems; Computational/AI modeling 1. Introduction Consider automatic altitude correction systems in air- planes or simply the task to keep different bank accounts at a certain levels. In both problems it is necessary to pre- dict and react on exogenous changes, i.e. changes that can- not be influenced by the controller and which have a hidden dynamic. Often the task is to maintain a certain goal level (e.g. a bank account should not be negative) by manipulating components of the system. A simplified version of such a control task is the micro world dynamic stocks and flows (DSF) developed by Dutt and Gonzalez (2007). This task has been used to study human behavior in controlling a dynamic system consist- ing of repeated decision situations as demonstrated in Fig. 1 (an overview can be found in Gonzalez, Vanyukov, & Martin (2005)). The classical DSF-task consists of a water tank containing a certain amount of water and four connected flows (two inflows and two outflows) through which water can flow into or out of the tank and change the amount of water. One inflow and one outflow can be controlled by a controller whereas the other two are controlled exogenously, i.e. they are defined by the envi- ronment only. The underlying dynamic of the environ- mental flows is defined by computable functions. The task of the controller is to reach or maintain a specific goal configuration, i.e. a specific amount of the water in the tank. Dutt and Gonzales used a computer version of this task for psychological experiments to study how humans behave in this scenario. This version has a visual represen- tation of the water tank as well as numerical representa- tions of system attributes like the current water level, the goal amount and recent values for the four flows. From a cognitive perspective, the task of participants was to recognize and to predict the behavior of the exoge- nous flows and using this information to compute counter- balancing actions for reaching or maintaining the goal amount over a time period of 100 time steps. The hidden environmental flows can be values of any computable function. For example, the inflow could be 1389-0417/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cogsys.2010.12.008 ⇑ Corresponding author. E-mail addresses: ragni@cognition.uni-freiburg.de (M. Ragni), felix. steffenhagen@cognition.uni-freiburg.de (F. Steffenhagen), Andreas. Klein@cognition.uni-freiburg.de (A. Klein). www.elsevier.com/locate/cogsys Available online at www.sciencedirect.com Cognitive Systems Research 12 (2011) 309–320