Behavioral and Brain Sciences

Processing capacity defined by relational complexity: Implications for comparative, developmental, and cognitive psychology

Graeme S. Halford a1, William H. Wilson a2 and Steven Phillips a3
a1 Department of Psychology, University of Queensland, Brisbane, Queensland 4072, Australia [email protected]
a2 Department of Computer Science & Engineering, University of New South Wales, Sydney, New South Wales, Australia [email protected]
a3 Information Science Division, Electrotechnical Laboratory, Tsukuba 305, Japan [email protected] [email protected]/welcome.html


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.

Key Words: capacity limits; chunking; cognitive development; comparative psychology; complexity; neural nets; relations; representations; resources; working memory.