Neural representations of magnitude for natural and rational numbers

DeWolf, Melissa; Chiang, Jeffrey N.; Bassok, Miriam; Holyoak, Keith J.; Monti, Martin M.

doi:10.1016/j.neuroimage.2016.07.052

Cited by 23 publications

(23 citation statements)

References 52 publications

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“…First, we assessed the simple effect of load for deductive (D) and non‐deductive (ND) trials (i.e., [complex > simple] ND and [complex > simple] D ), and, following, we assessed the interaction effect of load and task type (i.e., [complex – simple] ND > [complex – simple] D and [complex – simple] D > [complex – simple] ND ). In order to avoid reverse activations (Morcom & Fletcher, ), each contrast was masked to only include voxels for which the sum of the z‐score statistic of the minuend and subtrahend was equal to or greater than zero (cf., DeWolf, Chiang, Bassok, Holyoak, and Monti, ). For the simple effect of load in deduction, for example, the mask was created by only including voxels for which

true[z_{{(|, C o m p l e x - F i x)}_{D}} + z_{{(|, S i m p l e - F i x)}_{D}} \geq 0 true]

while, for the interaction effect the mask was created by only including voxels for which

true[z_{{true(C o m p l e x - S i m p l e true)}_{D}} + z_{{true(C o m p l e x - S i m p l e true)}_{N D}} \geq 0

].…”

Section: Methodsmentioning

confidence: 99%

“…For the simple effect of load in deduction, for example, the mask was created by only including voxels for which

true[z_{{(|, C o m p l e x - F i x)}_{D}} + z_{{(|, S i m p l e - F i x)}_{D}} \geq 0 true]

while, for the interaction effect the mask was created by only including voxels for which

true[z_{{true(C o m p l e x - S i m p l e true)}_{D}} + z_{{true(C o m p l e x - S i m p l e true)}_{N D}} \geq 0

]. This procedure ensures that a voxel cannot be found active merely because the subtrahend is negative (i.e., less active than baseline/fixation) while the minuend is not greater than zero (i.e., not more active than baseline/fixation; see DeWolf et al, ).…”

Section: Methodsmentioning

confidence: 99%

“…ND ). In order to avoid reverse activations(Morcom & Fletcher, 2007), each contrast was masked to only include voxels for which the sum of the z-score statistic of the minuend and subtrahend was equal to or greater than zero (cf., DeWolf, Chiang, Bassok, Holyoak, andMonti, 2016). For the simple effect of load in deduction, for example, the mask was created…”

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confidence: 99%

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At the core of reasoning: Dissociating deductive and non‐deductive load

Coetzee

Monti

2018

Human Brain Mapping

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In recent years, neuroimaging methods have been used to investigate how the human mind carries out deductive reasoning. According to some, the neural substrate of language is integral to deductive reasoning. According to others, deductive reasoning is supported by a language-independent distributed network including left frontopolar and frontomedial cortices. However, it has been suggested that activity in these frontal regions might instead reflect non-deductive factors such as working memory load and general cognitive difficulty. To address this issue, 20 healthy volunteers participated in an fMRI experiment in which they evaluated matched simple and complex deductive and non-deductive arguments in a 2 × 2 design. The contrast of complex versus simple deductive trials resulted in a pattern of activation closely matching previous work, including frontopolar and frontomedial "core" areas of deduction as well as other "cognitive support" areas in frontoparietal cortices. Conversely, the contrast of complex and simple non-deductive trials resulted in a pattern of activation that does not include any of the aforementioned "core" areas. Direct comparison of the load effect across deductive and non-deductive trials further supports the view that activity in the regions previously interpreted as "core" to deductive reasoning cannot merely reflect non-deductive load, but instead might reflect processes specific to the deductive calculus. Finally, consistent with previous reports, the classical language areas in left inferior frontal gyrus and posterior temporal cortex do not appear to participate in deductive inference beyond their role in encoding stimuli presented in linguistic format.

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true[z_{{(|, C o m p l e x - F i x)}_{D}} + z_{{(|, S i m p l e - F i x)}_{D}} \geq 0 true]

while, for the interaction effect the mask was created by only including voxels for which

true[z_{{true(C o m p l e x - S i m p l e true)}_{D}} + z_{{true(C o m p l e x - S i m p l e true)}_{N D}} \geq 0

].…”

Section: Methodsmentioning

confidence: 99%

“…For the simple effect of load in deduction, for example, the mask was created by only including voxels for which

true[z_{{(|, C o m p l e x - F i x)}_{D}} + z_{{(|, S i m p l e - F i x)}_{D}} \geq 0 true]

while, for the interaction effect the mask was created by only including voxels for which

true[z_{{true(C o m p l e x - S i m p l e true)}_{D}} + z_{{true(C o m p l e x - S i m p l e true)}_{N D}} \geq 0

Section: Methodsmentioning

confidence: 99%

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At the core of reasoning: Dissociating deductive and non‐deductive load

Coetzee

Monti

2018

Human Brain Mapping

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“…The ability to estimate with decimals appears to involve the same type of analog mental number line used with whole numbers (e.g., Dehaene & Changeux, 1993;DeWolf et al, 2014;DeWolf et al, 2016). For fractions, magnitude estimates are far less precise and require additional mental calculation, as people must perform a rough approximation to division (DeWolf et al, 2014;Fazio, DeWolf, & Siegler, 2016;Kallai & Tzelgov, 2009), or else some other error-prone componential strategy (Bonato et al, 2007;Fazio et al, 2016).…”

Section: Processing Strategies For Quantitative Reasoningmentioning

confidence: 99%

Reasoning strategies with rational numbers revealed by eye tracking

Plummer

DeWolf

Bassok

et al. 2017

Atten Percept Psychophys

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Recent research has begun to investigate the impact of different formats for rational numbers on the processes by which people make relational judgments about quantitative relations. DeWolf, Bassok, and Holyoak (Journal of Experimental Psychology: General, 144(1), 2015) found that accuracy on a relation identification task was highest when fractions were presented with countable sets, whereas accuracy was relatively low for all conditions where decimals were presented. However, it is unclear what processing strategies underlie these disparities in accuracy. We report an experiment that used eye-tracking methods to externalize the strategies that are evoked by different types of rational numbers for different types of quantities (discrete vs. continuous). Results showed that eye-movement behavior during the task was jointly determined by image and number format. Discrete images elicited a counting strategy for both fractions and decimals, but this strategy led to higher accuracy only for fractions. Continuous images encouraged magnitude estimation and comparison, but to a greater degree for decimals than fractions. This strategy led to decreased accuracy for both number formats. By analyzing participants' eye movements when they viewed a relational context and made decisions, we were able to obtain an externalized representation of the strategic choices evoked by different ontological types of entities and different types of rational numbers. Our findings using eye-tracking measures enable us to go beyond previous studies based on accuracy data alone, demonstrating that quantitative properties of images and the different formats for rational numbers jointly influence strategies that generate eye-movement behavior.

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“…The basic logic was to use BART and baseline models to predict degrees of relation similarity, and then to correlate predictions of the models with patterns of neural similarity in regions of interest. We examined three types of abstract relations (similar, contrast, cause-purpose), with three specific We employed a sequential event-related fMRI design (23) to separate the construction of first-order relations (i.e., relations between words in a pair) from the second-order assessment of similarity between relations (i.e., the analogical match between A:B and C:D relations) (see Timing of events on each trial. Participants were shown two word pairs, first an A:B pair for 2 seconds, then a C:D pair for 2 seconds after a jitter, and finally a cue to make a yes/no decision about the validity of the analogy.…”

Section: Introductionmentioning

confidence: 99%

Distributed Code for Semantic Relations Predicts Neural Similarity

Chiang¹,

Peng²,

Lu³

et al. 2019

Preprint

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The ability to generate and process semantic relations is central to many aspects of human cognition. Theorists have long debated whether such relations are coded as atomistic links in a semantic network, or as distributed patterns over some core set of abstract relations.The form and content of the conceptual and neural representations of semantic relations remains to be empirically established. The present study combined computational modeling and neuroimaging to investigate the representation and comparison of abstract semantic relations in the brain. By using sequential presentation of verbal analogies, we decoupled the neural activity associated with encoding the representation of the first-order semantic relation between words in a pair from that associated with the second-order comparison of two relations. We tested alternative computational models of relational similarity in order to distinguish between rival accounts of how semantic relations are coded and compared in the brain. Analyses of neural similarity patterns supported the hypothesis that semantic relations are coded, in the parietal cortex, as distributed representations over a pool of abstract relations specified in a theory-based taxonomy. These representations, in turn, provide the immediate inputs to the process of analogical comparison, which draws on a broad frontoparietal network. This study sheds light not only on the form of relation representations but also on their specific content.Significance: Relations provide basic building blocks for language and thought. For the past half century, cognitive scientists exploring human semantic memory have sought to identify the code for relations. In a neuroimaging paradigm, we tested alternative computational models of relation processing that predict patterns of neural similarity during distinct phases of analogical reasoning. The findings allowed us to draw inferences not only about the form of relation representations, but also about their specific content. The core of these distributed representations is based on a relatively small number of abstract relation types specified in a theory-based taxonomy. This study helps to resolve a longstanding debate concerning the nature of the conceptual and neural code for semantic relations in the mind and brain. Distributed Code for Relations

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Neural representations of magnitude for natural and rational numbers

Cited by 23 publications

References 52 publications

At the core of reasoning: Dissociating deductive and non‐deductive load

At the core of reasoning: Dissociating deductive and non‐deductive load

Reasoning strategies with rational numbers revealed by eye tracking

Distributed Code for Semantic Relations Predicts Neural Similarity

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