Annual Conference of the Australian Psychological Society, Canberra, October 3-7.
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Halford,
G.S. (2000) Analysis of Complexity in Cognitive Tasks. Keynote
Address to the 35th
Annual Conference of the Australian Psychological Society, Canberra, October 3-7. |
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Halford, G.S., Wilson, W.H., & Phillips, S. (1998). Processing capacity defined by relational complexity: Implications for comparative, developmental, and cognitive psychology. Behaviorial and Brain Sciences, 21(6), 803-831. |
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Halford, G. S., Bain, J. D., Maybery, M. T., & Andrews, G. (1998). Induction of relational schemas: Common processes in reasoning and complex learning. Cognitive Psychology, 35, 201-245. |
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Andrews, G., & Halford, G. S. (1998). Children's ability to make transitive inferences: The importance of premise integration and structural complexity. Cognitive Development, 13, 479-513 |
Andrews,
G., & Halford, G. S. (1998). Children's ability to make transitive
inferences: The importance of premise integration and structural complexity.
Cognitive
Development, 13, 479-513.
Four experiments were conducted to assess the ability of 4- to 6-year-olds
to make transitive inferences involving spatial relations. For example,
given premises, green higher than red; red higher than blue; the inference,
green higher than blue constitutes a transitive inference. In Experiment
1, 4-year-olds made marginally above-chance transitive inferences about
pairs of stacked blocks, but there was no generalization to tasks that
involved mapping from stacked blocks to sticks ordered from left to right,
or the reverse of this mapping. The 6-year-olds performed better, and were
above chance on both tasks. Experiments 2-4 showed a strong effect of complexity,
defined as number of relations processed in a single decision. In Experiment
2, younger children integrated two relations to make transitive inferences
at marginally above the one-relation baseline in the nonmapping but not
in the mapping condition. The 6-year-olds were above the baseline in both
conditions. In Experiment 3, 4-year-olds' performance was not significantly
better than the one-relation baseline in either condition, and this finding
was confirmed when data from equivalent conditions in Experiments 2 and
3 were combined. Experiment 4 produced further strong evidence for relational
complexity as the major determinant of childrenÕs difficulty in
transitive inference. Analysis of childrenÕs strategies indicated
a gradual development of the ability to integrate two binary relations
in a single decision. The percentage of children integrating two relations,
at least some of the time, increased from 20 % at age 4, to 53 % at age
5 and 57 % at age 6. The results were discussed in terms of relational
complexity as a domain-general factor in cognitive development.
Halford,
G. S., Bain, J. D., Maybery, M. T., & Andrews, G. (1998). Induction
of relational schemas: Common processes in reasoning and complex learning.
Cognitive
Psychology, 35, 201-245.
Five experiments were performed to test whether participants induced a coherent representation of the structure of a task, called a relational schema, from specific instances. Properties of a relational schema include: An explicit symbol for a relation, a binding that preserves the truth of a relation, potential for higher-order relations, omnidirectional access, potential for transfer between isomorphs, and ability to predict unseen items in isomorphic problems. However relational schemas are not necessarily coded in abstract form. Predictions from relational schema theory were contrasted with predictions from configural learning and other nonstructural theories in five experiments in which participants were taught a structure comprised of a set of initial-state,operator Æ end-state instances. The initial-state,operator pairs were presented and participants had to predict the correct end-state. Induction of a relational schema was achieved efficiently by adult participants as indicated by ability to predict items of a new isomorphic problem. The relational schemas induced showed the omnidirectional access property, there was efficient transfer to isomorphs, and structural coherence had a powerful effect on learning. The "learning to learn" effect traditionally associated with the learning set literature was observed, and the long-standing enigma of learning set acquisition is explained by a model composed of relational schema induction and structure mapping. Performance was better after reversal of operators than after shift to an alternate structure, even though the latter entailed more overlap with previously learned tasks in terms of the number of configural associations that were preserved. An explanation for the reversal shift phenomenon in terms of induction and mapping of a relational schema is proposed. The five experiments provided evidence supporting predictions from relational schema theory, and no evidence was found for configural or nonstructural learning theories.
Halford,
G.S., Wilson, W.H., & Phillips, S. (1998). Processing capacity defined
by relational complexity: Implications for comparative, developmental,
and cognitive psychology. Behaviorial and Brain Sciences, 21(6), 803-831.
It is argued that working memory limitations are best defined in terms of the complexity of relations that can be processed in parallel. Relational complexity is related to processing loads in problem solving, and discriminates between higher animal species, as well as between children of different ages. Complexity is defined by the number of dimensions, or sources of variation, that are related. A unary relation has one argument and one source of variation, because its argument can be instantiated in only one way at a time. A binary relation has two arguments, and two sources of variation, because two argument instantiations are possible at once. Similarly, a ternary relation is three dimensional, a quaternary relation is four dimensional, and so on. Dimensionality is related to number of chunks, because both attributes on dimensions and chunks are independent units of information of arbitrary size. Empirical studies of working memory limitations indicate a soft limit which corresponds to processing one quaternary relation in parallel. More complex concepts are processed by segmentation or conceptual chunking. Segmentation entails breaking tasks into components which do not exceed processing capacity, and which are processed serially. Conceptual chunking entails "collapsing" representations to reduce their dimensionality and consequently their processing load, but at the cost of making some relational information inaccessible. Parallel distributed processing implementations of relational representations show that relations with more arguments entail a higher computational cost, which corresponds to empirical observations of higher processing loads in humans. Empirical evidence is presented that relational complexity discriminates between higher species, is related to processing load in reasoning and in sentence comprehension, and that the complexity of relations processed by children increases with age. Implications are considered for neural net models, and for theories of cognition and cognitive development.