Overlapping and distinct neural representations of numbers and verbal transitive series

Seeing inferences: brain dynamics and oculomotor signatures of non-verbal deduction

We often express our thoughts through words, but thinking goes well beyond language. Here we focus on an elementary but basic thinking process, disjunction elimination, elicited by elementary visual scenes deprived of linguistic content, describing its neural and oculomotor correlates. We track two main components of a nonverbal deductive process: the construction of a logical representation (A or B), and its simplification by deduction (not A, therefore B). We identify the network active in the two phases and show that in the latter, but not in the former, it overlaps with areas known to respond to verbal logical reasoning. Oculomotor markers consistently differentiate logical processing induced by the construction of a representation, its simplification by deductive inference, and its maintenance when inferences cannot be drawn. Our results reveal how integrative logical processes incorporate novel experience in the flow of thoughts induced by visual scenes.

Neurocognitive basis of deductive reasoning in children varies with parental education

The neurocognitive basis of elementary academic skills varies with parental socioeconomic status (SES). Little is known, however, about SES‐related differences underlying higher‐order cognitive skills that are critical for school success, such as reasoning. Here we used fMRI to examine how the neurocognitive basis of deductive reasoning varies as a function of parental education in school‐aged children. Higher parental education was associated with greater reliance on the left inferior frontal gyrus when solving set‐inclusion problems, consistent with other work suggesting that these problems might more heavily rely on verbal systems in the brain. In addition, children who are at the lower end of the parental education continuum, but have higher nonverbal skills relied on right parietal areas to a greater degree than their peers for solving set‐inclusion problems. Finally, lower parental education children with higher verbal or nonverbal skill engaged dorsolateral prefrontal regions to a greater degree for set‐inclusion and linear‐order relations than their peers. These findings suggest that children with lower parental education rely on spatial and cognitive control mechanisms to achieve parity with their peers with parents who have more education. Better understanding variability in the neurocognitive networks that children recruit as a function of their parental factors might benefit future individualized interventions that best match children's characteristics.

Deductive-reasoning brain networks: A coordinate-based meta-analysis of the neural signatures in deductive reasoning

OBJECTIVE

Deductive reasoning is a complex and poorly understood concept in the field of psychology. Many cognitive neuroscience studies have been published on deductive reasoning but have yielded inconsistent findings.

METHODS

In this study, we analyzed collected data from 38 articles using a recently proposed activation likelihood estimation (ALE) approach and used conjunction analysis to better determine the intersection of the results of meta-analyses.

RESULTS

First, the left hemispheres in the inferior parietal lobule (Brodmann area 40 [BA40]), middle frontal gyrus (BA6), medial frontal gyrus (BA8), inferior frontal gyrus (BA45/46), caudate, and insula (BA47) were revealed to be significant brain regions via simple-effect analysis (deductive reasoning versus baseline). Furthermore, IFG, insula, and cingulate (the key neural hubs of the cingulo-opercular network) were highlighted in overlapped functional connectivity maps.

CONCLUSION

The findings of the current study are consistent with the view that deductive reasoning requires a succession of stages, which included decoding of linguistic information, conversion and correction of rules, and transformation of inferential results into conclusive outputs, all of which are putatively processed via a distributed network of brain regions encompassing frontal/parietal cortices, as well as the caudate and other subcortical structures, which suggested that in the process of deductive reasoning, the coding and integration of premise information is indispensable, and it is also crucial to the execution and monitoring of the cognitive processing of reasoning.

Learned Representation of Implied Serial Order in Posterior Parietal Cortex

Monkeys can learn the implied ranking of pairs of images drawn from an ordered set, despite never seeing all of the images simultaneously and without explicit spatial or temporal cues. We recorded the activity of posterior parietal cortex (including lateral intraparietal area LIP) neurons while monkeys learned 7-item transitive inference (TI) lists with 2 items presented on each trial. Behavior and neuronal activity were significantly influenced by the ordinal relationship of the stimulus pairs, specifically symbolic distance (the difference in rank) and joint rank (the sum of the ranks). Symbolic distance strongly predicted decision accuracy and learning rate. An effect of joint rank on performance was found nested within the symbolic distance effect. Across the population of neurons, there was significant modulation of firing correlated with the relative ranks of the two stimuli presented on each trial. Neurons exhibited selectivity for stimulus rank during learning, but not before or after. The observed behavior is poorly explained by associative or reward mechanisms, and appears more consistent with a mental workspace model in which implied serial order is mapped within a spatial framework. The neural data suggest that posterior parietal cortex supports serial learning by representing information about the ordinal relationship of the stimuli presented during a given trial.

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.

The Neural Correlates of Relational Reasoning: A Meta-analysis of 47 Functional Magnetic Resonance Studies

It is a core cognitive ability of humans to represent and reason about relational information, such as “the train station is north of the hotel” or “Charles is richer than Jim.” However, the neural processes underlying the ability to draw conclusions about relations are still not sufficiently understood. Central open questions are as follows: (1) What are the neural correlates of relational reasoning? (2) Where can deductive and inductive reasoning be localized? (3) What is the impact of different informational types on cerebral activity? For that, we conducted a meta-analysis of 47 neuroimaging studies. We found activation of the frontoparietal network during both deductive and inductive reasoning, with additional activation in an extended network during inductive reasoning in the basal ganglia and the inferior parietal cortex. Analyses revealed a double dissociation concerning the lateral and medial Brodmann's area 6 during deductive and inductive reasoning, indicating differences in terms of processing verbal information in deductive and spatial information in inductive tasks. During semantic and symbolic tasks, the frontoparietal network was found active, whereas geometric tasks only elicited prefrontal activation, which can be explained by the reduced demand for the construction of a mental representation in geometric tasks. Our study provides new insights into the cognitive mechanisms underlying relational reasoning and clarifies previous controversies concerning involved brain areas.

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.

Origins of the brain networks for advanced mathematics in expert mathematicians

The origins of human abilities for mathematics are debated: Some theories suggest that they are founded upon evolutionarily ancient brain circuits for number and space and others that they are grounded in language competence. To evaluate what brain systems underlie higher mathematics, we scanned professional mathematicians and mathematically naive subjects of equal academic standing as they evaluated the truth of advanced mathematical and nonmathematical statements. In professional mathematicians only, mathematical statements, whether in algebra, analysis, topology or geometry, activated a reproducible set of bilateral frontal, Intraparietal, and ventrolateral temporal regions. Crucially, these activations spared areas related to language and to general-knowledge semantics. Rather, mathematical judgments were related to an amplification of brain activity at sites that are activated by numbers and formulas in nonmathematicians, with a corresponding reduction in nearby face responses. The evidence suggests that high-level mathematical expertise and basic number sense share common roots in a nonlinguistic brain circuit.

Reasoning from transitive premises: an EEG study

Neuroimaging studies have contributed to a major advance in understanding the neural and cognitive mechanisms underpinning deductive reasoning. However, the dynamics of cognitive events associated with inference making have been largely neglected. Using electroencephalography, the present study aims at describing the rapid sequence of processes involved in performing transitive inference (A B; B C therefore "A C"; with AB meaning "A is to the left of B"). The results indicate that when the second premise can be integrated into the first one (e.g. A B; B C) its processing elicits a P3b component. In contrast, when the second premise cannot be integrated into the first premise (e.g. A B; D C), a P600-like components is elicited. These ERP components are discussed with respect to cognitive expectations.

Is order the defining feature of magnitude representation? An ERP study on learning numerical magnitude and spatial order of artificial symbols

Using an artificial-number learning paradigm and the ERP technique, the present study investigated neural mechanisms involved in the learning of magnitude and spatial order. 54 college students were divided into 2 groups matched in age, gender, and school major. One group was asked to learn the associations between magnitude (dot patterns) and the meaningless Gibson symbols, and the other group learned the associations between spatial order (horizontal positions on the screen) and the same set of symbols. Results revealed differentiated neural mechanisms underlying the learning processes of symbolic magnitude and spatial order. Compared to magnitude learning, spatial-order learning showed a later and reversed distance effect. Furthermore, an analysis of the order-priming effect showed that order was not inherent to the learning of magnitude. Results of this study showed a dissociation between magnitude and order, which supports the numerosity code hypothesis of mental representations of magnitude.

Thought beyond language: neural dissociation of algebra and natural language

A central question in cognitive science is whether natural language provides combinatorial operations that are essential to diverse domains of thought. In the study reported here, we addressed this issue by examining the role of linguistic mechanisms in forging the hierarchical structures of algebra. In a 3-T functional MRI experiment, we showed that processing of the syntax-like operations of algebra does not rely on the neural mechanisms of natural language. Our findings indicate that processing the syntax of language elicits the known substrate of linguistic competence, whereas algebraic operations recruit bilateral parietal brain regions previously implicated in the representation of magnitude. This double dissociation argues against the view that language provides the structure of thought across all cognitive domains.

Fractionating the neural substrates of transitive reasoning: task-dependent contributions of spatial and verbal representations

It has long been suggested that transitive reasoning relies on spatial representations in the posterior parietal cortex (PPC). Previous neuroimaging studies, however, have always focused on linear arguments, such as "John is taller than Tom, Tom is taller than Chris, therefore John is taller than Chris." Using functional magnetic resonance imaging (fMRI), we demonstrate here that verbal representations contribute to transitive reasoning when it involves set-inclusion relations (e.g., "All Tulips are Flowers, All Flowers are Plants, therefore All Tulips are Plants"). In the present study, such arguments were found to engage verbal processing regions of the left inferior frontal gyrus (IFG) and left PPC that were identified in an independent localizer task. Specifically, activity in these verbal regions increased as the number of relations increased in set-inclusion arguments. Importantly, this effect was specific to set-inclusion arguments because left IFG and left PPC were not differentially engaged when the number of relations increased in linear arguments. Instead, such an increase was linked to decreased activity in a spatial processing region of the right PPC that was identified in an independent localizer task. Therefore, both verbal and spatial representations can underlie transitive reasoning, but their engagement depends upon the structure of the argument.

Distinct representations of subtraction and multiplication in the neural systems for numerosity and language

It has been proposed that recent cultural inventions such as symbolic arithmetic recycle evolutionary older neural mechanisms. A central assumption of this hypothesis is that the degree to which a preexisting mechanism is recycled depends on the degree of similarity between its initial function and the novel task. To test this assumption, we investigated whether the brain region involved in magnitude comparison in the intraparietal sulcus (IPS), localized by a numerosity comparison task, is recruited to a greater degree by arithmetic problems that involve number comparison (single-digit subtractions) than by problems that involve retrieving number facts from memory (single-digit multiplications). Our results confirmed that subtractions are associated with greater activity in the IPS than multiplications, whereas multiplications elicit greater activity than subtractions in regions involved in verbal processing including the middle temporal gyrus (MTG) and inferior frontal gyrus (IFG) that were localized by a phonological processing task. Pattern analyses further indicated that the neural mechanisms more active for subtraction than multiplication in the IPS overlap with those involved in numerosity comparison and that the strength of this overlap predicts interindividual performance in the subtraction task. These findings provide novel evidence that elementary arithmetic relies on the cooption of evolutionary older neural circuits.

Logic, language and the brain

What is the role of language in human cognition? Within the domain of deductive reasoning, the issue has been the focus of numerous investigations without the emergence of a consensus view. Here we consider some of the reasons why neuroimaging studies of deductive reasoning have generated mixed results. We then review recent evidence suggesting that the role of language in deductive reasoning is confined to an initial stage in which verbally presented information is encoded as non-verbal representations. These representations are then manipulated by mental operations that are not based on the neural mechanisms of natural language. This article is part of a Special Issue entitled "The Cognitive Neuroscience".

The brain network for deductive reasoning: a quantitative meta-analysis of 28 neuroimaging studies

Over the course of the past decade, contradictory claims have been made regarding the neural bases of deductive reasoning. Researchers have been puzzled by apparent inconsistencies in the literature. Some have even questioned the effectiveness of the methodology used to study the neural bases of deductive reasoning. However, the idea that neuroimaging findings are inconsistent is not based on any quantitative evidence. Here, we report the results of a quantitative meta-analysis of 28 neuroimaging studies of deductive reasoning published between 1997 and 2010, combining 382 participants. Consistent areas of activations across studies were identified using the multilevel kernel density analysis method. We found that results from neuroimaging studies are more consistent than what has been previously assumed. Overall, studies consistently report activations in specific regions of a left fronto-parietal system, as well as in the left BG. This brain system can be decomposed into three subsystems that are specific to particular types of deductive arguments: relational, categorical, and propositional. These dissociations explain inconstancies in the literature. However, they are incompatible with the notion that deductive reasoning is supported by a single cognitive system relying either on visuospatial or rule-based mechanisms. Our findings provide critical insight into the cognitive organization of deductive reasoning and need to be accounted for by cognitive theories.

Gaze modulates non-propositional reasoning: further evidence for spatial representation of reasoning premises

Human and animals are able to decide that A>C after having learnt that A>B and B>C. This basic property of logical thinking has been studied by transitive inference (TI) tasks. It has been hypothesized that subjects displace the premises of the inference on a mental line to solve the task. An evidence in favor of this interpretation is the observation of the symbolic distance effect, that is the improvement of the performance as the distance between items increases. This effect has been interpreted as support to the hypothesis that ability to perform TI tasks follows the same rules and is mediated by the same brain circuits involved in the performance of spatial tasks. We tested ten subjects performing a TI on an ordered list of Japanese characters while they were fixating either leftwards or rightwards, to evaluate whether the eye position modulated the performance in making TI as it does in spatial tasks. Our results show a significant linear decrease of the reaction time with the increase of the symbolic distance and a shift of this trend towards lower reaction times when subjects were fixating to the left. We interpret this eye position effect as a further evidence that spatial and reasoning tasks share the same underlying mechanisms and neural substrates. The eye position effect also points to a parietal cortex involvement in the neural circuit involved in transitive reasoning.