![]() ![]() Tower defense (TD) games ask players to protect a base by organizing the base’s defenses. In addition to providing insights on human reasoning, and providing strategies for implementation in an agent, compu- tational models of space and time have many practical ap- plications, such as urban planning. ![]() TD problems contain no “hidden variables” and the potential interactions of space and time – though sometimes nonobvious and subtle – are open for observation. ![]() Our work differs from computer-based complex scenarios or microworlds, used to study dynamic decision making and complex problem solving (Gonzalez, Vanyukov, and Martin 2005), in which people actively interact with an unknown (nontransparent) system of many highly interrelated variables so as to actively generate knowledge to achieve certain goals. In this study we are not aiming at creating a model of human spatiotemporal reasoning, but by understanding how humans handle spatiotemporal problems we provide the foundations for de- signing agents capable of replicating human performance. An ACT-R model of simple human spatial relational reasoning has been developed (Ragni and Brüssow 2011). 2004), which models low-level operations and mental resources and can be used to predict task difficulty and performance time. Understanding mental models is essential to create cognitive models, such as ACT-R (Anderson et al. Specifically, we examine how humans reason about the motions of objects in 2D that move at different speeds. Time is conflated with one-dimensional space, but in this paper we address how humans reason about temporal effects of actions performed in a two dimensional space. Time typically is mapped to one dimensional space, for instance, moving from left to right, or from back to front, to repre- sent the passage of time (Miles et al. When people think about time, they use whatever spatial representation is cognitively available to them. Similar effects have been shown for problems that require both temporal and spatial reasoning (Vandierendonck and Vooght 1997), creating strong sup- port for how humans use mental models. Specifically, when people use temporal relations to assess the relative order of events, having a single mental model reduces process- ing time and increases accuracy (Schaeken, Johnson-Laird, and d’Ydewalle 1996). Problems that require multiple mental models are harder for people. Research suggests that simpler mental models are preferred over more complex models for making deductions because the inference process is easier (Johnson-Laird 2001 Jahn and Knauff 1998). Previous work has studied spatial representations used by people, such as the mental spatial maps con- structed for navigation tasks (Kuipers 1978), and representations used in naive physics models for predicting the out- come of an action (Friedman and Forbus 2009). ![]()
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