A diffusion model analysis of belief bias: Different cognitive mechanisms explain how cognitive abilities and thinking styles contribute to conflict resolution in reasoning

Recent results have challenged the widespread assumption of dual process models of belief bias that sound reasoning relies on slow, careful reflection, whereas biased reasoning is based on fast intuition. Instead, parallel process models of reasoning suggest that rule- and belief-based problem features are processed in parallel and that reasoning problems that elicit a conflict between rule- and belief-based problem features may also elicit more than one Type 1 response. This has important implications for individual-differences research on reasoning, because rule-based responses by certain individuals may reflect that these individuals were either more likely to give a rule-based default response or that they successfully inhibited and overrode a belief-based default response. In two studies, we used the diffusion model to describe decision making in a transitive reasoning task. In Study 1, 41 participants were asked to evaluate conclusions based on their validity. In Study 2, 133 participants evaluated conclusions based on their validity or believability. We tested which diffusion model parameters reflected conflict resolution and related those model parameters to individual differences in cognitive abilities and thinking styles. Individual differences in need for cognition predicted successful conflict resolution under logic instruction, which suggests that a disposition to engage in reflective thinking facilitates the inhibition and override of Type 1 responses. Intelligence, however, was negatively related to successful conflict resolution under belief instruction, which suggests that individuals with high cognitive abilities quickly generated a higher-level logical response that interfered with their ability to evaluate lower-level intrinsic problem features. Taken together, this double dissociation indicates that cognitive abilities and thinking styles affect the processing of conflict information through different mechanisms and at different stages: Greater cognitive abilities facilitate the efficient creation of decoupled problem representations, whereas a greater disposition to engage in critical thinking facilitates the detection and override of Type 1 responses.

Towards a resolution of some outstanding issues in transitive research: An empirical test on middle childhood

Transitive Inference (deduce B > D from B > C and C > D) can help us to understand other areas of sociocognitive development. Across three experiments, learning, memory, and the validity of two transitive paradigms were investigated. In Experiment 1 (N = 121), 7-year-olds completed a three-term nontraining task or a five-term task requiring extensive-training. Performance was superior on the three-term task. Experiment 2 presented 5–10-year-olds with a new five-term task, increasing learning opportunities without lengthening training (N = 71). Inferences improved, suggesting children can learn five-term series rapidly. Regarding memory, the minor (CD) premise was the best predictor of BD-inferential performance in both task-types. However, tasks exhibited different profiles according to associations between the major (BC) premise and BD inference, correlations between the premises, and the role of age. Experiment 3 (N = 227) helped rule out the possible objection that the above findings simply stemmed from three-term tasks with real objects being easier to solve than computer-tasks. It also confirmed that, unlike for five-term task (Experiments 1 & 2), inferences on three-term tasks improve with age, whether the age range is wide (Experiment 3) or narrow (Experiment 2). I conclude that the tasks indexed different routes within a dual-process conception of transitive reasoning: The five-term tasks indexes Type 1 (associative) processing, and the three-term task indexes Type 2 (analytic) processing. As well as demonstrating that both tasks are perfectly valid, these findings open up opportunities to use transitive tasks for educability, to investigate the role of transitivity in other domains of reasoning, and potentially to benefit the lived experiences of persons with developmental issues.

Neural representations of transitive relations predict current and future math calculation skills in children

A large body of evidence suggests that math learning in children is built upon innate mechanisms for representing numerical quantities in the intraparietal sulcus (IPS). Learning math, however, is about more than processing quantitative information. It is also about understanding relations between quantities and making inferences based on these relations. Consistent with this idea, recent behavioral studies suggest that the ability to process transitive relations (A > B, B > C, therefore A > C) may contribute to math skills in children. Here we used fMRI coupled with a longitudinal design to determine whether the neural processing of transitive relations in children could predict their current and future math skills. At baseline (T₁), children (n = 31) processed transitive relations in an MRI scanner. Math skills were measured at T₁ and again 1.5 years later (T₂). Using a machine learning approach with cross-validation, we found that activity associated with the representation of transitive relations in the IPS predicted math calculation skills at both T₁ and T₂. Our study highlights the potential of neurobiological measures of transitive reasoning for forecasting math skills in children, providing additional evidence for a link between this type of reasoning and math learning.

Ease and control: the cognitive benefits of hierarchy

This review identifies two cognitive benefits of social hierarchy that may contribute to hierarchy maintenance. First, research indicates that people pay attention to hierarchies automatically, early, and accurately. As a result, hierarchies feel easy to process, which increases liking and support of hierarchy. Second, through their clear, predictable structures and the opportunities they provide for personal agency, hierarchies help people satisfy their need for control, which may lead people to seek out and maintain hierarchy, especially if they currently hold a high rank or believe in social mobility. These cognitive benefits of ease and control may have effects on the performance of hierarchies and on people's willingness to change unfair structures.

Impaired neural processing of transitive relations in children with math learning difficulty

Math learning difficulty (i.e., MLD) is common in children and can have far-reaching consequences in personal and professional life. Converging evidence suggests that MLD is associated with impairments in the intraparietal sulcus (IPS). However, the role that these impairments play in MLD remains unclear. Although it is often assumed that IPS deficits affect core numerical abilities, the IPS is also involved in several non-numerical processes that may contribute to math skills. For instance, the IPS supports transitive reasoning (i.e., the ability to integrate relations such as A > B and B > C to infer that A > C), a skill that is central to many aspects of math learning in children. Here we measured fMRI activity of 8- to 12-year-olds with MLD and typically developing (TD) peers while they listened to stories that included transitive relations. Children also answered questions evaluating whether transitive inferences were made during story comprehension. Compared to non-transitive relations (e.g., A > B and C > D), listening to transitive relations (e.g., A > B and B > C) was associated with enhanced activity in the IPS in TD children. In children with MLD, the difference in activity between transitive and non-transitive relations in the IPS was (i) non-reliable and (ii) smaller than in TD children. Finally, children with MLD were less accurate than TD peers when making transitive inferences based on transitive relations. Thus, a deficit in the online processing of transitive relations in the IPS might contribute to math difficulties in children with MLD.

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Transitive reasoning is central to mathematical thinking.

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Transitive reasoning relies on the intra-parietal sulcus (IPS) in healthy children.

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Math learning difficulty (MLD) is associated with IPS impairments.

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Transitive reasoning is impaired in children with MLD.

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Transitive reasoning does not engage the IPS in children with MLD.

Factors and processes in children's transitive deductions

Transitive tasks are important for understanding how children develop socio-cognitively. However, developmental research has been restricted largely to questions surrounding maturation. We asked 6-, 7- and 8-year-olds (N = 117) to solve a composite of five different transitive tasks. Tasks included conditions asking about item-C (associated with the marked relation) in addition to the usual case of asking only about item-A (associated with the unmarked relation). Here, children found resolving item-C much easier than resolving item-A, a finding running counter to long-standing assumptions about transitive reasoning. Considering gender perhaps for the first time, boys exhibited higher transitive scores than girls overall. Finally, analysing in the context of one recent and well-specified theory of spatial transitive reasoning, we generated the prediction that reporting the full series should be easier than deducing any one item from that series. This prediction was not upheld. We discuss amendments necessary to accommodate all our earlier findings.

Transitive inference of social dominance by human infants

It is surprising that there are inconsistent findings of transitive inference (TI) in young infants given that non-linguistic species succeed on TI tests. To conclusively test for TI in infants, we developed a task within the social domain, with which infants are known to show sophistication. We familiarized 10- to 13-month-olds (M = 11.53 months) to a video of two dominance interactions between three puppets (bear > elephant; hippo > bear) consistent with a dominance hierarchy (hippo > bear > elephant; where '>' denotes greater dominance). Infants then viewed interactions between the two puppets that had not interacted during familiarization. These interactions were either congruent (hippo > elephant) or incongruent (elephant > hippo) with the inferred hierarchy. Consistent with TI, infants looked longer to incongruent than congruent displays. Control conditions ruled out the possibility that infants' expectations were based on stable behaviors specific to individual puppets rather than their inferred transitive dominance relations. We suggest that TI may be supported by phylogenetically ancient mechanisms of ordinal representation and visuospatial processing that come online early in human development.

Transfer of a serial representation between two distinct tasks by rhesus macaques

Do animals form task-specific representations, or do those representations take a general form that can be applied to qualitatively different tasks? Rhesus monkeys (Macaca mulatta) learned the ordering of stimulus lists using two different serial tasks, in order to test whether prior experience in each task could be transfered to the other, enhancing performance. The simultaneous chaining paradigm delivered rewards only after subjects responded in the correct order to all stimuli displayed on a touch sensitive video monitor. The transitive inference paradigm presented pairs of items and delivered rewards when subjects selected the item with the lower ordinal rank. After learning a list in one paradigm, subjects' knowledge of that list was tested using the other paradigm. Performance was enhanced from the very start of transfer training. Transitive inference performance was characterized by 'symbolic distance effects,' whereby the ordinal distance between stimuli in the implied list ordering was strongly predictive of the probability of a correct response. The patterns of error displayed by subjects in both tasks were best explained by a spatially coded representation of list items, regardless of which task was used to learn the list. Our analysis permits properties of this representation to be investigated without the confound of verbal reasoning.

Medial temporal lobe memory in childhood: developmental transitions

The medial temporal lobes (MTL) support declarative memory and mature structurally and functionally during the postnatal years in humans. Although recent work has addressed the development of declarative memory in early childhood, less is known about continued development beyond this period of time. The purpose of this investigation was to explore MTL-dependent memory across middle childhood. Children (6 -10 years old) and adults completed two computerized tasks, place learning (PL) and transitive inference (TI), that each examined relational memory, as well as the flexible use of relational learning. Findings suggest that the development of relational memory precedes the development of the ability to use relational knowledge flexibly in novel situations. Implications for the development of underlying brain areas and ideas for future neuroimaging investigations are discussed.

Nonverbal transitive inference: Effects of task and awareness on human performance

We studied human nonverbal transitive inference in two paradigms: with choice stimuli orderable along a physical dimension and with non-orderable choice stimuli. We taught 96 participants to discriminate four overlapping pairs of choice stimuli: A+ B-, B+ C-, C+ D-, and D+ E-. Half of the participants were provided with post-choice visual feedback stimuli which were orderable by size; the other half were not provided with orderable feedback stimuli. In later testing, we presented novel choice pairs: BD, AC, AD, AE, BE, and CE. We found that transitive responding depended on task awareness for all participants. Additionally, participants given ordered feedback showed clearer task awareness and stronger transitive responding than did participants not given ordered feedback. Associative models (Wynne, 1995; Siemann and Delius, 1998) failed to predict the increase in transitive responding with increasing awareness. These results suggest that ordered and non-ordered transitive inference tasks support different patterns of performance.

Darwin's mistake: Explaining the discontinuity between human and nonhuman minds

Over the last quarter century, the dominant tendency in comparative cognitive psychology has been to emphasize the similarities between human and nonhuman minds and to downplay the differences as “one of degree and not of kind” (Darwin 1871). In the present target article, we argue that Darwin was mistaken: the profound biological continuity between human and nonhuman animals masks an equally profound discontinuity between human and nonhuman minds. To wit, there is a significant discontinuity in the degree to which human and nonhuman animals are able to approximate the higher-order, systematic, relational capabilities of a physical symbol system (PSS) (Newell 1980). We show that this symbolic-relational discontinuity pervades nearly every domain of cognition and runs much deeper than even the spectacular scaffolding provided by language or culture alone can explain. We propose a representational-level specification as to where human and nonhuman animals' abilities to approximate a PSS are similar and where they differ. We conclude by suggesting that recent symbolic-connectionist models of cognition shed new light on the mechanisms that underlie the gap between human and nonhuman minds.

Primate errors in transitive ‘inference’: a two-tier learning model

Transitive performance (TP) is a learning-based behaviour exhibited by a wide range of species, where if a subject has been taught to prefer A when presented with the pair AB but to prefer B when presented with the pair BC, then the subject will also prefer A when presented with the novel pair AC. Most explanations of TP assume that subjects recognize and learn an underlying sequence from observing the training pairs. However, data from squirrel monkeys (Saimiri sciureus) and young children contradict this, showing that when three different items (a triad) are drawn from the sequence, subjects' performance degrades systematically (McGonigle and Chalmers, Nature 267:694-696, 1977; Chalmers and McGonigle, Journal of Experimental Child Psychology 37:355-377, 1984; Harris and McGonigle, The Quarterly Journal of Experimental Psychology 47B:319-348, 1994). We present here the two-tier model, the first learning model of TP which accounts for this systematic performance degradation. Our model assumes primate TP is based on a general-purpose task learning system rather than a special-purpose sequence-learning system. It supports the hypothesis of Heckers et al. (Hippocampus 14:153-162, 2004) that TP is an expression of two separate general learning elements: one for associating actions and contexts, another for prioritising associations when more than one context is present. The two-tier model also provides explanations for why phased training is important for helping subjects learn the initial training pairs and why some subjects fail to do so. It also supports the Harris and McGonigle (The Quarterly Journal of Experimental Psychology 47B:319-348, 1994) explanation of why, once the training pairs have been acquired, subjects perform transitive choice automatically on two-item diads, but not when exposed to triads from the same sequence.

Effect of stimulus orderability and reinforcement history on transitive responding in pigeons

Transitive responding in humans and non-human animals has attracted considerable attention because of its presumably inferential nature. In an attempt to replicate our earlier study with crows [Lazareva, O.F., Smirnova, A.A., Bagozkaja, M.S., Zorina, Z.A., Rayevsky, V.V., Wasserman, E.A., 2004. Transitive responding in hooded crows requires linearly ordered stimuli. J. Exp. Anal. Behav. 82, 1-19], we trained pigeons to discriminate overlapping pairs of colored squares (A+ B-, B+ C-, C+ D-, and D+ E-). For some birds, the colored squares, or primary stimuli, were followed by a circle of the same color (feedback stimuli) whose diameter decreased from A to E (Ordered Feedback group); these circles were made available to help order the stimuli along a physical dimension. For other birds, all of the feedback stimuli had the same diameter (Constant Feedback group). In later testing, novel choice pairs were presented, including the critical BD pair. The pigeons' reinforcement history with Stimuli B and D was controlled, so that the birds should not have chosen Stimulus B during the BD test. Unlike the crows, the pigeons selected Stimulus B over Stimulus D in both ordered and Constant Feedback groups, suggesting that the orderability of the post-choice feedback stimuli did not affect pigeons' transitive responding. Post hoc simulations showed that associative models [Wynne, C.D.L., 1995. Reinforcement accounts for transitive inference (TI) performance. Anim. Learn. Behav. 23, 207-217; Siemann, M., Delius, J.D., 1998. Algebraic learning and neural network models for transitive and non-transitive responding. Eur. J. Cogn. Psychol. 10, 307-334] failed to predict pigeons' responding in the BD test.

On aims and methods in the neuroimaging of derived relations

Ingenious and seemingly powerful technologies have been developed recently that enable the visualization in some detail of events in the brain concomitant upon the ongoing behavioral performance of a human participant. Measurement of such brain events offers at the very least a new set of dependent variables in relation to which the independent variables familiarly manipulated in the operant laboratory may be explored. Two related paradigms in which a start has been made in such research concern the derivation of novel or emergent relations from a baseline set of trained relations, and include the phenomenon of transitive inference (TI), observed in studies of stimulus equivalence (SE) and serial learning (SL) or seriation. This paper reviews some published and forthcoming neuroimaging studies of these and related phenomena, and considers how this line of research both demands and represents a welcome synthesis between types of question and levels of explanation in behavioral science that often have been seen as antithetical.

Transitive responding in hooded crows requires linearly ordered stimuli

Eight crows were taught to discriminate overlapping pairs of visual stimuli (A+ B-, B+ C-, C+ D-, and D+ E-). For 4 birds, the stimuli were colored cards with a circle of the same color on the reverse side whose diameter decreased from A to E (ordered feedback group). These circles were made available for comparison to potentially help the crows order the stimuli along a physical dimension. For the other 4 birds, the circles corresponding to the colored cards had the same diameter (constant feedback group). In later testing, a novel choice pair (BD) was presented. Reinforcement history involving stimuli B and D was controlled so that the reinforcement/nonreinforcement ratios for the latter would be greater than for the former. If, during the BD test, the crows chose between stimuli according to these reinforcement/nonreinforcement ratios, then they should prefer D; if they chose according to the diameter of the feedback stimuli, then they should prefer B. In the ordered feedback group, the crows strongly preferred B over D; in the constant feedback group, the crows' choice did not differ significantly from chance. These results, plus simulations using associative models, suggest that the orderability of the postchoice feedback stimuli is important for crows' transitive responding.

The role of cues to differential absolute size in children's transitive inferences

To investigate the role that "nonlogical" cues might play in transitive inference, 6- and 7-year-olds were given a three-term transitive task in which perceptual cues to differential absolute size were either present or absent. Relationships between the taught premises and the relational information that was physically present were manipulated using four basic conditions: "congruent," "inverse," "pretended," or "persuaded." Both age groups showed identical overall premise memory, but the younger group tended to reason more on the basis of the perceptual information rather than on the successfully encoded premise information. Contrasts between the various conditions showed that categorical effects can be circumvented in three-term problems with appropriate controls, that there may be qualitative as well as quantitative differences in transitive inference with age, and that transitive inference is not based solely on memory. The findings also indicate that, although 7-year-olds are competent in "logic-based" transitive inference, they experience great difficulty on tasks involving pretend information.