Graeme S. Halford

• Griffith University

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 syntactic analy...

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 repres...

The Wason Selection Task (WST) is a well-known test of reasoning in which one turns over cards to test a rule about the two faces. Modifications were made to the WST to enable more direct and analytical investigation of reasoning processes. The modifications included extensive training to reduce variations in task interpretation, isolation of worki...

Relational complexity (RC) is a metric reflecting capacity limitation in relational processing. It plays a crucial role in higher cognitive processes and is an endophenotype for several disorders. However, the genetic underpinnings of complex relational processing have not been investigated. Using the classical twin model, we estimated the heritabi...

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...

A proposal for a categorization of cognition based on core properties of the constituent processes that integrates theory and empirical findings across domains. 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 d...

Rhodes and Brandone (2014) have shown evidence of limited theory of mind in 3-year old children. The study was based on a false belief procedure in which an observer [E1] saw a toy hidden in location 1, then it was moved to location 2. E1 observed the move in the true belief (TB) test but not in the false belief (FB) test. Then the child was assess...

Objective: The research examined whether verbal learning and memory impairment previously observed 1 year after left hemisphere stroke endures over a longer period and whether stroke sufferers compensate for their impairments using working memory. Methodology: Twenty-one persons with left hemisphere lesions; 20 with right hemisphere lesions only...

This chapter describes a consistent view of executive control. It offers evidence that a major function of an executive is to support relational processing involved in planning, reasoning and comprehension. Humans are generally limited to relating four variables in a cognitive representation, though a minority of adults can relate five variables. T...

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 ada...

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 reason...

In this article, we sought to isolate the processing demands of combining the concepts of modifier‐noun phrases from those of other language comprehension processes. Probe reaction time (RT) was used as an indication of the processing resources required for combining concepts. Phrase frequency (as measured by Google hit rates) was used as a metric...

The research examined relational processing following stroke. Stroke patients (14 with frontal, 30 with non-frontal lesions) and 41 matched controls completed four relational processing tasks: sentence comprehension, Latin square matrix completion, modified Dimensional Change Card Sorting, and n-back. Each task included items at two or three levels...

Two experiments examined conditional discrimination in 4- to 6-year-olds. Children learned to choose one of two objects (e.g., circle) when the background was, say, red and to choose the other object (e.g., triangle) when the background was, say, blue. Awareness was assessed and interpreted as a marker of relational processing. In Experiment 1, mos...

Three levels of mathematical concepts are outlined. Level 1 consists of concepts which depend on binary relations and unary operations. Level 2 consists of concepts which can be encoded as binary operations, and Level 3 consists of concepts which can be expressed as compositions of binary operations. Three levels of cognitive development which corr...

A group of non-conservers underwent learning set training designed to induce acquisition of conservation by teaching the necessary relationships for it to be inferred. In the training group 14 out of 16 Ss attained conservation, whereas only 4 out of 16 controls did so. Then all Ss were given training designed to convice them that two initially equ...

The effect of an uninformative tone on the bar-pressing behaviour of rats was studied to see whether a secondary reinforcer had any role beyond that of signal of a forthcoming reward. A tone was sounded for 1 sec. immediately following each bar press by the experimental group. After a delay, 50 per cent of bar presses were followed by a food pellet...

Rats were trained to press a bar in a Skinner box and were then given food pellets independently of the bar presses. In one group of rats, a tone followed each bar press, and another occurrence of the same tone preceded the delivery of the food pellet. A second group had the tone following bar press but no tone preceding food pellets. The third gro...

Explanations of the difficulty of relative-clause sentences implicate complexity but the measurement of complexity remains controversial. Four experiments investigated how far relational complexity (RC) theory, that has been found valid for cognitive development and human reasoning, accounts for the difficulty of 16 types of English, object- and su...

Accumulating evidence on the nature, function and acquisition of relational knowledge indicates a crucial role of such knowledge in higher cognitive processes. In this review, we specify the essential properties of relational knowledge, together with the role it plays in reasoning, categorisation, planning, quantification and language. Furthermore,...

Neo-Piagetian ModelsAttempts at SynthesisProcessing SpeedCognitive ComplexityLevels of Cognitive FunctioningProcess Models of Cognitive DevelopmentRelational Knowledge and AnalogySymbolic Neural Net ModelsConclusion References

The complexity of categorical syllogisms was assessed using the relational complexity metric, which is based on the number of entities that are related in a single cognitive representation. This was compared with number of mental models in an experiment in which adult participants solved all 64 syllogisms. Both metrics accounted for similarly large...

Duality (0.09 MB PDF)

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 structure...

Young children's integration of weight and distance information was examined using a new methodology that combines a single-armed apparatus with functional measurement. Weight and distance values were varied factorially across the item set. Children estimated how far the beam would tilt when different numbers of weights were placed at different dis...

Bayesian rationality is an important contribution to syllogistic inference, but it has limitations. The claim that confidence in a conclusion is a function of informativeness of the max-premise is anomalous because this is the least probable premise. A more plausible account is that confidence is inversely related to complexity. Bayesian rationalit...

Graeme Halford has worked in several universities in Australia and Canada. He was awarded a personal chair at the University of Queensland in 1989, where he is now an adjunct professor, and he is also a professor of psychology at Griffith University. He has published approximately 100 technical works, including articles in Behavioral and Brain Scie...

The assumption of some developmental theories that short-term memory is the workspace of higher cognitive processes, and consequently that span measures processing capacity, is claimed to be inconsistent with the working memory literature. 4 experiments, using children aged 5 to 12 years, contrast this theory with a model in which short-term memory...

We propose that the missing link from nonhuman to human cognition lies with our ability to form, modify, and re-form dynamic bindings between internal representations of world-states. This capacity goes beyond dynamic feature binding in perception and involves a new conception of working memory. We propose two tests for structured knowledge that mi...

Neo-Piagetian ModelsProcessing SpeedCognitive ComplexityLevels of Cognitive FunctioningProcess Models of Cognitive DevelopmentRelational Knowledge and AnalogySymbolic Neural Net ModelsConclusion

According to cognitive complexity and control (CCC) theory complexity depends on number of levels of a hierarchy of rules. According to relational complexity (RC) theory complexity is a function of the number of related variables in the task, and the most difficult tasks are those in which there is a constraint on decomposition into simpler subtask...

The Children's Gambling Task (CGT, Kerr & Zelazo, 2004) involves integrating information about losses and gains to maximize winnings when selecting cards from two decks. Both Cognitive Complexity and Control (CCC) theory and Relational Complexity (RC) theory attribute younger children's difficulty to task complexity. In CCC theory, identification o...

We propose that working memory and reasoning share related capacity limits. These limits are quantified in terms of the number of items that can be kept active in working memory, 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 load...

Yes Yes

Participants learned about a structure without explicit explanation, either by using relational schema induction (G. S. Halford, J. D. Bain, M. T. Maybery, & G. Andrews, 1998), which requires completion of instances of the structure, or by memorizing instances. Emergence of structured knowledge over trials was assessed by ability to map the structu...

Theoretical analyses of air traffic complexity were carried out using the Method for the Analysis of Relational Complexity. Twenty-two air traffic controllers examined static air traffic displays and were required to detect and resolve conflicts. Objective measures of performance included conflict detection time and accuracy. Subjective perceptions...

Previous research has indicated that the cognitive load imposed by tasks in various content domains increases with the complexity of the relational information processed. Sentence comprehension entails processing noun-verb relations to determine who did what to whom. The difficulty of object-extracted relative clause sentences might stem from the c...

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 identificati...

The Relcon algorithm models category formation using relational storage and retrieval mechanisms with a Tensor memory. Relcon settles on a category structure that matches prototypicality characteristics of human categories. A tensor intersection operation simulates the influence of context on category structure and on similarity. The results have i...

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...

Current conceptions of the nature of human reasoning make it no longer tenable to assess children's inference by reference to the norms of logical inference. Alternatively, the complexity of the mental models employed in children's inferences can be analysed. This approach is applied to transitive inference, class inclusion, categorical induction,...

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 effect...

Children aged between 3 and 7 years were taught simple and dimension-abstracted oddity discrimination using learning-set training techniques, in which isomorphic problems with varying content were presented with verbal explanation and feedback. Following the training phase, simple oddity (SO), dimension-abstracted oddity with one or two irrelevant...

Two experiments tested predictions from a theory in which processing load depends on relational complexity (RC), the number of variables related in a single decision. Tasks from six domains (transitivity, hierarchical classification, class inclusion, cardinality, relative-clause sentence comprehension, and hypothesis testing) were administered to c...

Three experiments investigated the effect of complexity on children's understanding of a beam balance. In nonconflict problems, weights or distances varied, while the other was held constant. In conflict items, both weight and distance varied, and items were of three kinds: weight dominant, distance dominant, or balance (in which neither was domina...

Hierarchical classification (HC) and category induction (CI) were tested by a common property inference procedure to facilitate comparison and enable relative complexities to be assessed. Relational complexity theory predicts that HC is more complex because it entails a ternary relation between categories B, A, and A' such that A and A' are include...

An application of the Method of Analysis of Relational Complexity (MARC) to suppositional reasoning in the knight—knave task is outlined. The task requires testing suppositions derived from statements made by individuals who either always tell the truth or always lie. Relational complexity (RC) is defined as the number of unique entities that need...

at it has sometimes been difficult to demonstrate its effects on human problem solving in the laboratory. Analogy is a structure-preserving map from a base or source to a target (Gentner, 1983) but unless participants are given extensive training on the base analog, they tend to focus on superficial attributes rather than recognising relations that...

If a person knows that Fred ate a pizza, then they can answer the following questions: Who ate a pizza?, What did Fred eat?, What did Fred do to the pizza? and even Who ate what? This and related properties we are terming accessibility properties for the relational fact that Fred ate a pizza. Accessibility in this sense is a significant property of...

Analogy has been the focus of extensive research in cognitive science over the past two decades. Through analogy, novel situations and problems can be understood in terms of familiar ones. Indeed, a case can be made for analogical processing as the very core of cognition. This is the first book to span the full range of disciplines concerned with a...

Cowan's review shows that a short-term memory limit of four items is consistent with a wide range of phenomena in the field. However he does not explain that limit, whereas an existing theory does offer an explanation for capacity limitations. Furthermore processing capacity limits cannot be reduced to storage limits as Cowan claims. In his ex...

Infants often erroneously search for an object at a previously found location (A) despite seeing it hidden at a new location (B). Smith et al (1999) deny such A-notB errors arise from internal object-related conceptual states. Instead, they arise from the dynamics of goalrelated perception and action. We show that their model does not account for c...

A PDP model of human analogical reasoning is presented which is designed to incorporate psychologically realistic processing capacity limitations. Capacity is defined in terms of the complexity of relations that can be processed in parallel. Relations are represented in the model by computing the tensor product of vectors representing predicates an...

A mathematical basis is proposed for the distinction between associative and relational (symbolic) processing. Associations can be contrasted with relations in terms of ordered pairs versus general ordered N-tuples, and unidirectional access versus omnidirectional access. Relations also have additional properties: they can exhibit predicate-argumen...

Children's ability to modify their drawing procedures changes in their first decade. Young children make size/shape changes and end-of-sequence insertions /deletions of drawing elements. Older children also make middle-of-sequence insertions/deletions and position/orientation changes in drawing elements. Why do modifications occur in this order? We...

It is proposed that the distinction between basic and higher cognitive processes can be captured by the difference between associative and relational processes. Properties of relational processing include reification of the link between entities, so higher-order relations have lower-order relations as arguments, whereas an associative link per se c...

We argue that if a different definition of sentence complexity is adopted and processing capacity is assessed in a way that is consistent with that definition, then the Caplan & Waters distinction between interpretive versus postinterpretive processing is unnecessary insofar that it applies to the thematic role assignment in relative-clause sentenc...

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 binary 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...

The core issue of our target article concerns how relational complexity should be assessed. We propose that assessments must be based on actual cognitive processes used in performing each step of a task. Complexity comparisons are important for the orderly interpretation of research findings. The links between relational complexity theory and...

Four experiments investigated 4- to 6-year-olds' transitive inferences. In Experiments 1–3, there was a nonmapping condition in which inferences were made either about stacked blocks, or about sticks ordered left to right. In the mapping condition, inferences were made by mapping either from blocks to sticks, or the reverse. In Experiments 2–4, rel...

New concepts from cognitive science have fundamentally changed our view of cognitive development. In this paper we explore the implications of three concepts from cognitive science. These are learning (and induction), analogy, and capacity. New conceptions of learning have enabled us to understand how representations of the world are acquired. New...

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, omnidire...

Relational complexity has been found to be an effective metric for cognitive tasks. The hypothesis that the greater difficulty and later age of attainment of hierarchical classification as compared to category induction are attributable to differences in structural complexity was tested. Hierarchical classification entails a ternary relation betwee...

It is argued that abstract cognitive processes entail the processing of relations, which differ from more primitive cognitive processes in being more accessible, more flexible, and less content-specific. A relation is a binding between a relation-symbol or predicate, and one or more arguments. Each argument corresponds to a slot which can be filled...

At root, the systematicity debate over classical versus connectionist explanations for cognitive architecture turns on quantifying the degree to which human cognition is systematic. We introduce into the debate recent psychological data that provides strong support for the purely structure-based generalizations claimed by Fodor and Pylyshyn (1988)....

The distinction between uninformed learning (type-1) and learning based on recoding using prior information (type-2) helps to clarify some long-standing psychological problems, including misunderstanding of mathematics by children, the need for active construction of concepts in cognitive development, and the difficulty of configural learning...

Neural net models of human analogical reasoning need to incorporate realistic limitations in capacity to process information in parallel. Because of this, the STAR2 model, represents complex analogies as a hierarchy of levels, with parallel processing within any one level and serial processing between levels. The major components of the model are t...

The purpose of this project was to develop a psychologically realistic model of the way people construct a mapping between base and target domains in analogies. It was assumed that the mapping process was not based on an exhaustive search of possibilities, but that correspondences were first recognized between segments of each domain, then checked...

Originally published in Contemporary Psychology: APA Review of Books , 1996, Vol 41(3), 229-230. The reviewer contends that this book (see record 1993-99046-000 ) contains a rich descriptive account of the way children understand concepts such as intention, belief, desire, pretense, thought, and mental representation. It includes a chapter on autis...

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The reviewer contends that one of the perplexing aspects of psychology is that important relationships between areas of research sometimes seem to receive scant attention. One example is the relationship between psychometrics and cognitive development, which are related by both being concerned with intelligence. Mike Anderson's book (see record 199...

The relation between learning and development has been changed fundamentally by the advent of new conceptions of learning, induction, transfer, and strategy acquisition. Learning is no longer seen as simply the acquisition of behaviors. It also includes storing knowledge about relations in the world, as well as acquiring structural representations...

The assumption of some developmental theories that short-term memory is the workspace of higher cognitive processes, and consequently that span measures processing capacity, is claimed to be inconsistent with the working memory literature. 4 experiments, using children aged 5 to 12 years, contrast this theory with a model in which short-term memory...

There is now a reasonable amount of consensus that an analogy entails a mapping from one structure, the base or source, to another structure, the target (Gentner, 1983, 1989; Holyoak & Thagard, 1989). Theories of human analogical reasoning have been reviewed by Gentner (1989), who concludes that there is basic agreement on the one-to-one mapping of...

Creativity entails producing something which is both novel and effective. The novelty has to be genuine, so that whatever is produced would have been thought to be unlikely previously. A predictable variation on an already-known theme is not enough. A creative contribution also has to be effective, because many uncreative, even nonsensical ideas, c...

Cognitive development is driven by experience, but is mediated by domain general processes, which include learning, induction, and analogy. The concepts children understand, and the strategies they develop based on that understanding, depend on the complexity of the representation they can construct. Conceptual complexity can be defined in terms of...

Reviews "The Mind's Staircase: Exploring the Conceptual Underpinnings of Children's Thought and Knowledge," edited by Robbie Case. A main thesis of the book, which discusses theoretical issues and presents empirical evidence, is that children's cognitive development is guided by central conceptual structures, or networks of concepts that permit chi...

This is a description of one aspect of research carried out to assess and compare the processing loads of typical mathematical representations and strategies used by teachers and young children. The sample consisted of 29 children, aged between 5 and 8 years, and their teachers in a suburban school in a low to medium socioeconomic area in Brisbane,...

We take creativity to be an inherent aspect of the fundamental processes of cognition. Here we review models of two such processes - Humphreys, Bain and Pike's (1989) model of human memory and Halford, Wilson, Guo, Wiles and Stewart's (in press) tensor model of analogical mapping (STAR). In the memory model, information that has been stored in one...

This paper describes a computer-simulation model of the way in which basic reasoning processes develop in children. The model, based on PRISM-II programming language, was designed to reflect the manner in which world knowledge can be used to construct strategies for reasoning. The model learns strategies for performing transitive inference by using...

A range of factors affect human response to environmental change. They include the information available, understanding of the phenomenon, the nature of the decision‐making processes implied, and the motivation for change. One major factor affecting decision making is that scientific information is not fully and accurately disseminated through soci...

This paper describes a computer model that simulates the way children develop the reasoning skills of transitive inference and the construction of ordered sets. The computer model begins from general operations, such as setting and removing goals, storing and retrieving information, comparing elements to find matches, reading premises, and giving f...

This article addresses the question of whether information processing capacity is a factor in individual and developmental differences in readiness for learning. Other factors responsible for success in children's learning, such as strategies, encoding, and domain knowledge are examined. It is argued that although these factors are important, there...

Set size was varied as a factor in the primary memory paradigm developed by Wickens and colleagues (Wickens, Moody, & Dow, 1981; Wickens, Moody, & Vidulich, 1985). In Experiment 1, using adults and teenagers, no proactive interference (PI) was observed at set size 4, consistent with previous research, but PI was observed at set size 10. In Experime...

Three studies were conducted to investigate reasons for the difficulties that children under 5 years of age experience with class inclusion tasks. The studies tested the claim that such tasks have a structural complexity that is beyond the children's processing ability. In experiment 1, class inclusion tasks were compared with other classification...

Several contemporary theories of cognitive development appear to agree that children progress through a hierarchy of increasingly powerful cognitive organizations, and that higher-level organizations impose greater information-processing loads. Although theories differ in their method of defining both the levels and the information-processing loads...