Working memory limits are best defined in terms of the complexity of the relations that can be processed in parallel. Complexity is defined as the number of related dimensions or sources of variation. A unary relation has one argument and one source of variation; its argument can be instantiated in only one way at a time. A binary relation has two arguments, two sources of variation, and two instantiations, and so on. Dimensionality is related to the number of chunks, because both attributes on dimensions and chunks are independent units of information of arbitrary size. Studies of working memory limits suggest that there is a soft limit corresponding to the parallel processing of one quaternary relation. More complex concepts are processed by “segmentation” or “conceptual chunking.” In segmentation, tasks are broken into components that do not exceed processing capacity and can be processed serially. In conceptual chunking, representations are “collapsed” to reduce their dimensionality and hence their processing load, but at the cost of making some relational information inaccessible. Neural net models of relational representations show that relations with more arguments have a higher computational cost that coincides with experimental findings on higher processing loads in humans. Relational complexity is related to processing load in reasoning and sentence comprehension and can distinguish between the capacities of higher species. The complexity of relations processed by children increases with age. Implications for neural net models and theories of cognition and cognitive development are discussed.

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The conceptual complexity of problems was manipulated to probe the limits of human information processing capacity. Participants were asked to interpret graphically displayed statistical interactions. In such problems, all independent variables need to be considered together, so that decomposition into smaller subtasks is constrained, and thus the order of the interaction directly determines conceptual complexity. As the order of the interaction increases, the number of variables increases. Results showed a significant decline in accuracy and speed of solution from three-way to four-way interactions. Furthermore, performance on a five-way interaction was at chance level. These findings suggest that a structure defined on four variables is at the limit of human processing capacity.

We propose that working memory (WM) and reasoning share related capacity limits. These limits are quantified in terms of the number of items that can be kept active in WM, and the number of interrelationships between elements that can be kept active in reasoning. The latter defines the complexity of reasoning problems and the processing loads they impose. Principled procedures for measuring, controlling or limiting recoding and other strategies for reducing memory and processing loads have opened up new research opportunities, and yielded orderly quantification of capacity limits in both memory and reasoning. We argue that both types of limit may be based on the limited ability to form and preserve bindings between elements in memory.The techniques that humans have for making the best use of available information processing capacity are of immense value, but they have to be controlled in order to study capacity limitations and effects of complexity. New, principled procedures for measuring, controlling or limiting recoding and other strategies whereby subjects reduce memory and processing loads have enabled complexity and capacity effects to be investigated independently of, and in interaction with, knowledge. In this paper we present an hypothesis that this development enables a new, integrated treatment of reasoning and working memory (WM), including an orderly quantification of capacity limits, and that this has opened up new research opportunities. Working memory and reasoningDevelopments in both theory and methodology have strengthened the links between WM and reasoning and some salient points are summarised in Box 1. We propose that the essential link between WM and reasoning is in the common requirement to bind elements to a coordinate system. Consider first short-term serial recall of the words, "Fido, Rover, Cleo". The words are assigned to ordinal positions when presented ( Figure 1A), but this assignment must be maintained for later recall, and this requires attention. Even in free recall (not shown), items on a trial must be bound to the present-trial concept or node in memory; binding may be even more extensive inasmuch as an associative network between items would greatly aid in recall. Now consider a choice reaction time task where participants press a different button in response

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The ability to link variables is critical to many high-order cognitive functions, including reasoning. It has been proposed that limits in relating variables depend critically on relational complexity, defined formally as the number of variables to be related in solving a problem. In humans, the prefrontal cortex is known to be important for reasoning, but recent studies have suggested that such processes are likely to involve widespread functional brain networks. To test this hypothesis, we used functional magnetic resonance imaging and a classic measure of deductive reasoning to examine changes in brain networks as a function of relational complexity. As expected, behavioral performance declined as the number of variables to be related increased. Likewise, increments in relational complexity were associated with proportional enhancements in brain activity and task-based connectivity within and between 2 cognitive control networks: A cingulo-opercular network for maintaining task set, and a fronto-parietal network for implementing trial-by-trial control. Changes in effective connectivity as a function of increased relational complexity suggested a key role for the left dorsolateral prefrontal cortex in integrating and implementing task set in a trial-by-trial manner. Our findings show that limits in relational processing are manifested in the brain as complexity-dependent modulations of large-scale networks.

Relational complexity (RC) theory conceptualizes an individual’s processing capacity and a task’s complexity along a common ordinal metric. The authors describe the development of the Latin Square Task (LST) that assesses the influence of RC on reasoning. The LST minimizes the role of knowledge and storage capacity and thus refines the identification of a processing-capacity-related complexity effect in task performance. The LST is novel with one explicit rule that is easily understood by adults and children. In two studies, a test of 18 items encompassing three RC levels was administered to university ( N = 73; 16-33 years) and school ( N = 204; 8-19 years) students. Rasch analyses indicate that the LST scores were psychometrically stable across age groups and provides important diagnostic clues for task development. Consistent with RC theory, the LST is sensitive to parallel and serial (via segmentation) processing demands. The LST provides a strong basis for research on working memory and related constructs (fluid intelligence).

Cognitive complexity and control theory and relational complexity theory attribute developmental changes in theory of mind (TOM) to complexity. In 3 studies, 3-, 4-, and 5-year-olds performed TOM tasks (false belief, appearance-reality), less complex connections (Level 1 perspective-taking) tasks, and transformations tasks (understanding the effects of location changes and colored filters) with content similar to TOM. There were also predictor tasks at binary-relational and ternary-relational complexity levels, with different content. Consistent with complexity theories: (a) connections and transformations were easier and mastered earlier than TOM; (b) predictor tasks accounted for more than 80% of age-related variance in TOM; and (c) ternary-relational items accounted for TOM variance, before and after controlling for age and binary-relational items. Prediction did not require hierarchically structured predictor tasks.