Stochastic Independence between Recognition and Completion of Spatial Patterns as a Function of Causal Interpretation


A common view in the research on dynamic system control is that human subjects use exemplar knowledge of system states – at least for controlling small systems. Dissociations between different tasks or stochastic independence between recognition and control tasks, have led to the assumption that part of the exemplar knowledge is implicit. In this paper, I propose an alternative interpretation of these results by demonstrating that subjects learn more than exemplars when they are introduced to a new system. This was achieved by presenting the same material – states of a simple system – with vs. without causal interpretation. If subjects learned exemplars only, then there should be no differences between the conditions and stochastic dependence between various tasks would be expected. However, in an experiment with N=40 subjects the group with causal interpretation is significantly better at completing fragmentary system states and in judging causal relations between switches and lamps, but not in recognizing stimuli as studied. Only in the group without causal interpretation, the contingency between recognition and completion was close to the maximum memory dependence, estimated with Ostergaard’s (1992) method. Thus, the results resemble those of other studies only in the condition with causal interpretation. The results are explained by the assumption that subjects under that condition learn and use a second type of knowledge, which is construed as a rudimentary form of structural knowledge. The interpretation is supported by a computational model that is able to reproduce the set of results. Dynamic system control (DSC) is a paradigm of great interest for applied and basic research likewise. In applied contexts, researchers address questions about how human operators learn to operate new technical systems efficiently, how training should be designed, or what errors operators are likely to commit. In basic research, DSC is one of the paradigms for studying implicit learning. It has been argued that subjects control dynamic systems predominantly with exemplar knowledge about system states, part of which is considered implicit (Dienes & Fahey, 1998). This conclusion was derived from studies with systems characterized by small problem spaces, such as the “Sugar Factory” (a dynamic system with one input and one output variable, connected by a linear equation; Berry & Broadbent, 1988). However, studies with more complex systems have delivered evidence that structural knowledge (i.e. knowledge about the variables of a system and their causal relations) can be more effective for controlling these systems (Vollmeyer, Burns, & Holyoak, 1996; Funke, 1993), although it is not easy to apply and use this type of knowledge (Schoppek, 2002). But even for small systems, the question about what type of knowledge is learned in an implicit manner, is still open. Simulation studies that have proven the sufficiency of exemplar knowledge for controlling the Sugar Factory (Dienes & Fahey, 1995; Lebiere, Wallach, & Taatgen, 1998) have not yet reproduced effects that point to implicit learning. An example of such effects is the stochastic independence between recognition of system states of the Sugar Factory as studied and performance in one-step control problems, found by Dienes & Fahey (1998). Since exemplar knowledge is typically construed as explicit rather than implicit, it cannot account for these dissociations. This paper addresses the question if a rudimentary form of structural knowledge is acquired in addition to exemplar knowledge, albeit implicitly or explicitly. The different use of exemplar knowledge and structural knowledge in different tasks can explain dissociations between tasks. The basic strategy for separating the two Figure 1: Problem space of the Switches & Lamps system; the states with white triangles were studied in the learning phase knowledge types rests on using material that can be interpreted as states of a system or simply as spatial patterns. Therefore, I designed a system consisting of four lamps operated by four switches. Each switch affects one or two lamps. Two of the effects were negative, which means that the corresponding lamp is switched off when the switch is turned on. The problem space of 16 possible states is depicted in Figure 1. Subjects under both conditions (causal interpretation vs. no causal interpretation) are shown possible states and asked to memorize them. In a previous experiment with that paradigm (Schoppek, 2001), I found positive effects of causal interpretation on recognition of patterns as studied and on causal judgment. The effects were attributed to a preliminary form of structural knowledge, namely associations between switches and lamps, acquired by the group with causal interpretation. This knowledge enables subjects to reconstruct a system state in cases where no exemplar representation of the state can be retrieved. The pattern of results was reproduced by a computational model that instantiates these assumptions. The model is written in ACT-R (Anderson & Lebiere, 1998), a cognitive architecture that distinguishes between subsymbolic and symbolic levels of processing, with associative learning residing on the subsymbolic level. The experiment also delivered some hints that there was stochastic independence between recognition of states as studied and a completion task in the group with causal interpretation, but dependence in the other group. Again, this supports the assumption that more than one knowledge type is used in the causal condition. However, to judge an empirical contingency between tasks, it should be compared with the maximum possible memory dependence, estimated with a method proposed by Ostergaard (1992). This method requires answers to nonstudied items in the completion task, but all items that could be reasonably used in that task (i.e. all possible system states) have been studied in Schoppek (2001). Therefore in the present experiment, subjects studied only a subset of system states. This fact implies a different prediction for recognition of states as studied: The set of possible states and the set of studied states were identical in the previous experiment, whereas they are different in the present experiment. This makes the strategy of reconstructing system states susceptible to errors, because classifying any possible state as studied would result in many false alarms. Thus in the present experiment, I expect no differences in recognition performance between the two conditions.

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@inproceedings{Schoppek2002StochasticIB, title={Stochastic Independence between Recognition and Completion of Spatial Patterns as a Function of Causal Interpretation}, author={Wolfgang Schoppek}, year={2002} }