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"Halford, Graeme S"
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How Many Variables Can Humans Process?
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. Further-more, 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.
Journal Article
Planning Following Stroke: A Relational Complexity Approach Using the Tower of London
Planning on the 4-disk version of the Tower of London (TOL4) was examined in stroke patients and unimpaired controls. Overall TOL4 solution scores indicated impaired planning in the frontal stroke but not non-frontal stroke patients. Consistent with the claim that processing the relations between current states, intermediate states, and goal states is a key process in planning, the domain-general relational complexity metric was a good indicator of the experienced difficulty of TOL4 problems. The relational complexity metric shared variance with task-specific metrics of moves to solution and search depth. Frontal stroke patients showed impaired planning compared to controls on problems at all three complexity levels, but at only two of the three levels of moves to solution, search depth and goal ambiguity. Non-frontal stroke patients showed impaired planning only on the most difficult quaternary-relational and high search depth problems. An independent measure of relational processing (viz., Latin square task) predicted TOL4 solution scores after controlling for stroke status and location, and executive processing (Trail Making Test). The findings suggest that planning involves a domain-general capacity for relational processing that depends on the frontal brain regions.
Journal Article
What Do Transitive Inference and Class Inclusion Have in Common? Categorical (Co)Products and Cognitive Development
Transitive inference, class inclusion and a variety of other inferential abilities have strikingly similar developmental profiles-all are acquired around the age of five. Yet, little is known about the reasons for this correspondence. Category theory was invented as a formal means of establishing commonalities between various mathematical structures. We use category theory to show that transitive inference and class inclusion involve dual mathematical structures, called product and coproduct. Other inferential tasks with similar developmental profiles, including matrix completion, cardinality, dimensional changed card sorting, balance-scale (weight-distance integration), and Theory of Mind also involve these structures. By contrast, (co)products are not involved in the behaviours exhibited by younger children on these tasks, or simplified versions that are within their ability. These results point to a fundamental cognitive principle under development during childhood that is the capacity to compute (co)products in the categorical sense.
Journal Article
Categorizing Cognition
All sciences need ways to classify the phenomena they investigate; chemistry has the periodic table and biology a taxonomic system for classifying life forms. These classification schemes depend on conceptual coherence, demonstrated correspondences across paradigms. This conceptual coherence has proved elusive in psychology, although recent advances have brought the field to the point at which it is possible to define the type of classificatory system needed. This book proposes a categorization of cognition based on core properties of constituent processes, recognizing correspondences between cognitive processes with similar underlying structure but different surface properties. These correspondences are verified mathematically and shown not to be merely coincidental.The proposed formulation leads to general principles that transcend domains and paradigms and facilitate the interpretation of empirical findings. It covers human and nonhuman cognition and human cognition in all age ranges. Just as the periodic table classifies elements and not compounds, this system classifies relatively basic versions of cognitive tasks but allows for complexity. The book shows that a more integrated, coherent account of cognition would have many benefits. It would reduce the conceptual fragmentation of psychology; offer defined criteria by which to categorize new empirical results; and lead to fruitful hypotheses for the acquisition of higher cognition.
eBook
The Role of Working Memory in the Subsymbolic-Symbolic Transition
In this article, a proposal is made for a new account of the subsymbolic-to-symbolic transition based on a contemporary conception of working memory. Symbolic cognition is a constituent of reasoning and language and requires an operating system that is flexible and can produce novel, yet coherent, representations of relations that are useful in adapting to the environment. Acquisition of such an operating system depends on dynamic binding to a coordinate system in working memory. Recent studies with infants have indicated that this ability develops late in the 1st year of life, which corresponds to the time when symbols emerge in infant cognition. It also corresponds to the time when infants cease to make the A-not-B error, which depends on dynamic creation of a link in memory between an object and its location in space. We propose that such dynamic binding is a previously unrecognized marker of the symbolic transition. Emergence of symbolic processes (e.g., language, theory of mind) should be predicted longitudinally by dynamic binding to a coordinate system.
Journal Article
Theory of Mind and Relational Complexity
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.
Journal Article
Fundamental differences between perception and cognition aside from cognitive penetrability
Fundamental differences between perception and cognition argue that the distinction can be maintained independently of cognitive penetrability. The core processes of cognition can be integrated under the theory of relational knowledge. The distinguishing properties include symbols and an operating system, structure-consistent mapping between representations, construction of representations in working memory that enable generation of inferences, and different developmental time courses.
Journal Article
Resolving Conflicts Between Syntax and Plausibility in Sentence Comprehension
Comprehension of plausible and implausible object- and subject-relative clause sentences with and without prepositional phrases was examined. Undergraduates read each sentence then evaluated a statement as consistent or inconsistent with the sentence. Higher acceptance of consistent than inconsistent statements indicated reliance on
. Higher acceptance of plausible than implausible statements reflected reliance on
. There was greater reliance on semantic plausibility and lesser reliance on syntactic analysis for more complex object-relatives and sentences with prepositional phrases than for less complex subject-relatives and sentences without prepositional phrases. Comprehension accuracy and confidence were lower when syntactic analysis and semantic plausibility yielded conflicting interpretations. The conflict effect on comprehension was significant for complex sentences but not for less complex sentences. Working memory capacity predicted resolution of the
conflict in more and less complex items only when sentences and statements were presented sequentially. Fluid intelligence predicted resolution of the conflict in more and less complex items under sequential and simultaneous presentation. Domain-general processes appear to be involved in resolving syntax-plausibility conflicts in sentence comprehension.
Journal Article