Cognitive complexity explains processing asymmetry in judgments of similarity versus difference.

Human judgments of similarity and difference are sometimes asymmetrical, with the former being more sensitive than the latter to relational overlap, but the theoretical basis for this asymmetry remains unclear. We test an explanation based on the type of information used to make these judgments (relations versus features) and the comparison process itself (similarity versus difference). We propose that asymmetries arise from two aspects of cognitive complexity that impact judgments of similarity and difference: processing relations between entities is more cognitively demanding than processing features of individual entities, and comparisons assessing difference are more cognitively complex than those assessing similarity. In Experiment 1 we tested this hypothesis for both verbal comparisons between word pairs, and visual comparisons between sets of geometric shapes. Participants were asked to select one of two options that was either more similar to or more different from a standard. On unambiguous trials, one option was unambiguously more similar to the standard; on ambiguous trials, one option was more featurally similar to the standard, whereas the other was more relationally similar. Given the higher cognitive complexity of processing relations and of assessing difference, we predicted that detecting relational difference would be particularly demanding. We found that participants (1) had more difficulty detecting relational difference than they did relational similarity on unambiguous trials, and (2) tended to emphasize relational information more when judging similarity than when judging difference on ambiguous trials. The latter finding was replicated using more complex story stimuli (Experiment 2). We showed that this pattern can be captured by a computational model of comparison that weights relational information more heavily for similarity than for difference judgments.

Relational and lexical similarity in analogical reasoning and recognition memory: Behavioral evidence and computational evaluation.

We examined the role of different types of similarity in both analogical reasoning and recognition memory. On recognition tasks, people more often falsely report having seen a recombined word pair (e.g., flower: garden) if it instantiates the same semantic relation (e.g., is a part of) as a studied word pair (e.g., house: town). This phenomenon, termed relational luring, has been interpreted as evidence that explicit relation representations-known to play a central role in analogical reasoning-also impact episodic memory. We replicate and extend previous studies, showing that relation-based false alarms in recognition memory occur after participants encode word pairs either by making relatedness judgments about individual words presented sequentially, or by evaluating analogies between pairs of word pairs. To test alternative explanations of relational luring, we implemented an established model of recognition memory, the Generalized Context Model (GCM). Within this basic framework, we compared representations of word pairs based on similarities derived either from explicit relations or from lexical semantics (i.e., individual word meanings). In two experiments on recognition memory, best-fitting values of GCM parameters enabled both similarity models (even the model based solely on lexical semantics) to predict relational luring with comparable accuracy. However, the model based on explicit relations proved more robust to parameter variations than that based on lexical similarity. We found this same pattern of modeling results when applying GCM to an independent set of data reported by Popov, Hristova, and Anders (2017). In accord with previous work, we also found that explicit relation representations are necessary for modeling analogical reasoning. Our findings support the possibility that explicit relations, which are central to analogical reasoning, also play an important role in episodic memory.

Emergence of analogy from relation learning.

By middle childhood, humans are able to learn abstract semantic relations (e.g., antonym, synonym, category membership) and use them to reason by analogy. A deep theoretical challenge is to show how such abstract relations can arise from nonrelational inputs, thereby providing key elements of a protosymbolic representation system. We have developed a computational model that exploits the potential synergy between deep learning from "big data" (to create semantic features for individual words) and supervised learning from "small data" (to create representations of semantic relations between words). Given as inputs labeled pairs of lexical representations extracted by deep learning, the model creates augmented representations by remapping features according to the rank of differences between values for the two words in each pair. These augmented representations aid in coping with the feature alignment problem (e.g., matching those features that make "love-hate" an antonym with the different features that make "rich-poor" an antonym). The model extracts weight distributions that are used to estimate the probabilities that new word pairs instantiate each relation, capturing the pattern of human typicality judgments for a broad range of abstract semantic relations. A measure of relational similarity can be derived and used to solve simple verbal analogies with human-level accuracy. Because each acquired relation has a modular representation, basic symbolic operations are enabled (notably, the converse of any learned relation can be formed without additional training). Abstract semantic relations can be induced by bootstrapping from nonrelational inputs, thereby enabling relational generalization and analogical reasoning.

Relational Integration in the Human Brain: A Review and Synthesis.

Relational integration is required when multiple explicit representations of relations between entities must be jointly considered to make inferences. We provide an overview of the neural substrate of relational integration in humans and the processes that support it, focusing on work on analogical and deductive reasoning. In addition to neural evidence, we consider behavioral and computational work that has informed neural investigations of the representations of individual relations and of relational integration. In very general terms, evidence from neuroimaging, neuropsychological, and neuromodulatory studies points to a small set of regions (generally left lateralized) that appear to constitute key substrates for component processes of relational integration. These include posterior parietal cortex, implicated in the representation of first-order relations (e.g., A:B); rostrolateral pFC, apparently central in integrating first-order relations so as to generate and/or evaluate higher-order relations (e.g., A:B::C:D); dorsolateral pFC, involved in maintaining relations in working memory; and ventrolateral pFC, implicated in interference control (e.g., inhibiting salient information that competes with relevant relations). Recent work has begun to link computational models of relational representation and reasoning with patterns of neural activity within these brain areas.

Distributed Code for Semantic Relations Predicts Neural Similarity during Analogical Reasoning.

The ability to generate and process semantic relations is central to many aspects of human cognition. Theorists have long debated whether such relations are coarsely coded as links in a semantic network or finely coded as distributed patterns over some core set of abstract relations. The form and content of the conceptual and neural representations of semantic relations are yet to be empirically established. Using sequential presentation of verbal analogies, we compared neural activities in making analogy judgments with predictions derived from alternative computational models of relational dissimilarity to adjudicate among rival accounts of how semantic relations are coded and compared in the brain. We found that a frontoparietal network encodes the three relation types included in the design. A computational model based on semantic relations coded as distributed representations over a pool of abstract relations predicted neural activities for individual relations within the left superior parietal cortex and for second-order comparisons of relations within a broader left-lateralized network.

Cognitive and motivational factors driving sharing of internet memes.

As naturally occurring examples of folk culture and creativity, internet memes provide a rich testbed to examine the interrelationships among cognitive and motivational factors that influence their impact. In two studies with participants recruited over the internet, we measured a variety of appraisals of both apolitical and political memes with a focus on the role of metaphorical aptness and personal relatability as predictors of comprehensibility and humor. Structural equation modeling was used to analyze interconnections among appraisals. A major network path connects relatability to aptness, which in turn is linked to appraisals of comprehensibility, humor, and propensity to share. For political memes, the congruity of the meme with the person's political position (liberal or conservative) has a powerful but indirect impact on the propensity to share it. These findings indicate that appraisals of memes are based on cognitive and motivational processes that also underlie metaphor comprehension and appreciation of humor.

"But he's my brother": The impact of family obligation on moral judgments and decisions.

We created practical moral dilemmas for which participants imagined witnessing a transgression by a target person. The identity of the transgressor was manipulated to be either a stranger or the participant's brother. In Experiment 1, whether the target person committed a violation was left ambiguous. Participants made factual (how strongly they believe the target person actually committed a transgression) and unethicality judgments regarding the incident, and rated their willingness to report the transgressor to the police. Given ambiguity (Experiment 1), participants interpreted the facts in favor of their brother, but not in favor of a stranger. This interpretation led to moral judgments and willingness to report that favored family over strangers, while creating overall coherence in reasoning. In Experiment 2, we eliminated the ambiguity of the factual situation so that the possibility of achieving coherence between unethicality of an act and leniency toward a family member was blocked. Nonetheless, participants were less willing to report their brother to the police. Experiment 3 replicated the findings of the first two experiments within an integrated study design. Results from path analyses indicated that the factual judgment depended on factual understanding of an event, but willingness to report depended on identity of the target (i.e., brother vs. stranger), even at the cost of reduced coherence in reasoning. Moral decisions are thus strongly influenced by agent-relative obligations, such as duty to protect a family member.

Individual differences in relational reasoning.

Various forms of relational processing have been linked to cognitive capacity measures, such as working memory and fluid intelligence. However, previous work has not established the extent to which different forms of relational processing reflect common factors, nor whether individual differences in cognitive style also contribute to variations in relational reasoning. The current study took an individual-differences approach to investigate the prerequisites for relational processing. In two studies, college students completed a battery of standardized tests of individual differences related to fluid intelligence and cognitive style, as well as a series of experimental tasks that require relational reasoning. Moderate correlations were obtained between relational processing and measures of cognitive capacity. Questionnaire measures of cognitive style generally did not improve predictions of relational processing beyond the influence of measures of cognitive capacity.

Ex ante coherence shifts.

Cushman characterizes rationalization as the inverse of rational reasoning, but this distinction is psychologically questionable. Coherence-based reasoning highlights a subtler form of bidirectionality: By distorting task attributes to make one course of action appear superior to its rivals, a patina of rationality is bestowed on the choice. This mechanism drives choice and action, rather than just following in their wake.

Verbal analogy problem sets: An inventory of testing materials.

Analogical reasoning is an active topic of investigation across education, artificial intelligence (AI), cognitive psychology, and related fields. In all fields of inquiry, explicit analogy problems provide useful tools for investigating the mechanisms underlying analogical reasoning. Such sets have been developed by researchers working in the fields of educational testing, AI, and cognitive psychology. However, these analogy tests have not been systematically made accessible across all the relevant fields. The present paper aims to remedy this situation by presenting a working inventory of verbal analogy problem sets, intended to capture and organize sets from diverse sources.

Moral judgment as reasoning by constraint satisfaction.

May's careful examination of empirical evidence makes a compelling case against the primacy of emotion in driving moral judgments. At the same time, emotion certainly is involved in moral judgments. We argue that emotion interacts with beliefs, values, and moral principles through a process of coherence-based reasoning (operating at least partially below the level of conscious awareness) in generating moral judgments and decisions.

Countering antivaccination attitudes.

Three times as many cases of measles were reported in the United States in 2014 as in 2013. The reemergence of measles has been linked to a dangerous trend: parents refusing vaccinations for their children. Efforts have been made to counter people's antivaccination attitudes by providing scientific evidence refuting vaccination myths, but these interventions have proven ineffective. This study shows that highlighting factual information about the dangers of communicable diseases can positively impact people's attitudes to vaccination. This method outperformed alternative interventions aimed at undercutting vaccination myths.

The Love of Large Numbers: A Popularity Bias in Consumer Choice.

Social learning-the ability to learn from observing the decisions of other people and the outcomes of those decisions-is fundamental to human evolutionary and cultural success. The Internet now provides social evidence on an unprecedented scale. However, properly utilizing this evidence requires a capacity for statistical inference. We examined how people's interpretation of online review scores is influenced by the numbers of reviews-a potential indicator both of an item's popularity and of the precision of the average review score. Our task was designed to pit statistical information against social information. We modeled the behavior of an "intuitive statistician" using empirical prior information from millions of reviews posted on Amazon.com and then compared the model's predictions with the behavior of experimental participants. Under certain conditions, people preferred a product with more reviews to one with fewer reviews even though the statistical model indicated that the latter was likely to be of higher quality than the former. Overall, participants' judgments suggested that they failed to make meaningful statistical inferences.

Individual differences in spontaneous analogical transfer.

Research on analogical problem solving has shown that people often fail to spontaneously notice the relevance of a semantically remote source analog when solving a target problem, although they are able to form mappings and derive inferences when given a hint to recall the source. Relatively little work has investigated possible individual differences that predict spontaneous transfer, or how such differences may interact with interventions that facilitate transfer. In this study, fluid intelligence was measured for participants in an analogical problem-solving task, using an abridged version of the Raven's Progressive Matrices (RPM) test. In two experiments, we systematically compared the effect of augmenting verbal descriptions of the source with animations or static diagrams. Solution rates to Duncker's radiation problem were measured across varying source presentation conditions, and participants' understanding of the relevant source material was assessed. The pattern of transfer was best fit by a moderated mediation model: the positive impact of fluid intelligence on spontaneous transfer was mediated by its influence on source comprehension; however, this path was in turn modulated by provision of a supplemental animation via its influence on comprehension of the source. Animated source depictions were most beneficial in facilitating spontaneous transfer for those participants with low scores on the fluid intelligence measure.

Neural representations of magnitude for natural and rational numbers.

Humans have developed multiple symbolic representations for numbers, including natural numbers (positive integers) as well as rational numbers (both fractions and decimals). Despite a considerable body of behavioral and neuroimaging research, it is currently unknown whether different notations map onto a single, fully abstract, magnitude code, or whether separate representations exist for specific number types (e.g., natural versus rational) or number representations (e.g., base-10 versus fractions). We address this question by comparing brain metabolic response during a magnitude comparison task involving (on different trials) integers, decimals, and fractions. Univariate and multivariate analyses revealed that the strength and pattern of activation for fractions differed systematically, within the intraparietal sulcus, from that of both decimals and integers, while the latter two number representations appeared virtually indistinguishable. These results demonstrate that the two major notations formats for rational numbers, fractions and decimals, evoke distinct neural representations of magnitude, with decimals representations being more closely linked to those of integers than to those of magnitude-equivalent fractions. Our findings thus suggest that number representation (base-10 versus fractions) is an important organizational principle for the neural substrate underlying mathematical cognition.

Causal competition based on generic priors.

Although we live in a complex and multi-causal world, learners often lack sufficient data and/or cognitive resources to acquire a fully veridical causal model. The general goal of making precise predictions with energy-efficient representations suggests a generic prior favoring causal models that include a relatively small number of strong causes. Such "sparse and strong" priors make it possible to quickly identify the most potent individual causes, relegating weaker causes to secondary status or eliminating them from consideration altogether. Sparse-and-strong priors predict that competition will be observed between candidate causes of the same polarity (i.e., generative or else preventive) even if they occur independently. For instance, the strength of a moderately strong cause should be underestimated when an uncorrelated strong cause also occurs in the general learning environment, relative to when a weaker cause also occurs. We report three experiments investigating whether independently-occurring causes (either generative or preventive) compete when people make judgments of causal strength. Cue competition was indeed observed for both generative and preventive causes. The data were used to assess alternative computational models of human learning in complex multi-causal situations.

A set for relational reasoning: Facilitation of algebraic modeling by a fraction task.

Recent work has identified correlations between early mastery of fractions and later math achievement, especially in algebra. However, causal connections between aspects of reasoning with fractions and improved algebra performance have yet to be established. The current study investigated whether relational reasoning with fractions facilitates subsequent algebraic reasoning using both pre-algebra students and adult college students. Participants were first given either a relational reasoning fractions task or a fraction algebra procedures control task. Then, all participants solved word problems and constructed algebraic equations in either multiplication or division format. The word problems and the equation construction tasks involved simple multiplicative comparison statements such as "There are 4 times as many students as teachers in a classroom." Performance on the algebraic equation construction task was enhanced for participants who had previously completed the relational fractions task compared with those who completed the fraction algebra procedures task. This finding suggests that relational reasoning with fractions can establish a relational set that promotes students' tendency to model relations using algebraic expressions.

From rational numbers to algebra: separable contributions of decimal magnitude and relational understanding of fractions.

To understand the development of mathematical cognition and to improve instructional practices, it is critical to identify early predictors of difficulty in learning complex mathematical topics such as algebra. Recent work has shown that performance with fractions on a number line estimation task predicts algebra performance, whereas performance with whole numbers on similar estimation tasks does not. We sought to distinguish more specific precursors to algebra by measuring multiple aspects of knowledge about rational numbers. Because fractions are the first numbers that are relational expressions to which students are exposed, we investigated how understanding the relational bipartite format (a/b) of fractions might connect to later algebra performance. We presented middle school students with a battery of tests designed to measure relational understanding of fractions, procedural knowledge of fractions, and placement of fractions, decimals, and whole numbers onto number lines as well as algebra performance. Multiple regression analyses revealed that the best predictors of algebra performance were measures of relational fraction knowledge and ability to place decimals (not fractions or whole numbers) onto number lines. These findings suggest that at least two specific components of knowledge about rational numbers--relational understanding (best captured by fractions) and grasp of unidimensional magnitude (best captured by decimals)--can be linked to early success with algebraic expressions.

Far-out thinking: generating solutions to distant analogies promotes relational thinking.

Is it possible to induce a mind-set that will affect relational thinking in a subsequent reasoning task involving unrelated materials? We investigated whether evaluating the validity of verbal analogies (Experiment 1a) or generating solutions for them (Experiment 1b) could induce a relational mind-set that would transfer to an unrelated picture-mapping task. The verbal analogies were based on either near or far semantic relations. We found that generating (but not evaluating) solutions for semantically distant analogies increased the proportion of relational mappings on the transfer task, even after we controlled for fluid intelligence and response time. Solving near analogies did not produce transfer. Generation of solutions to far analogies appears to provide a potent method for triggering a mind-set that can enhance relational thinking in a different task.

The discovery and comparison of symbolic magnitudes.

Humans and other primates are able to make relative magnitude comparisons, both with perceptual stimuli and with symbolic inputs that convey magnitude information. Although numerous models of magnitude comparison have been proposed, the basic question of how symbolic magnitudes (e.g., size or intelligence of animals) are derived and represented in memory has received little attention. We argue that symbolic magnitudes often will not correspond directly to elementary features of individual concepts. Rather, magnitudes may be formed in working memory based on computations over more basic features stored in long-term memory. We present a model of how magnitudes can be acquired and compared based on BARTlet, a representationally simpler version of Bayesian Analogy with Relational Transformations (BART; Lu, Chen, & Holyoak, 2012). BARTlet operates on distributions of magnitude variables created by applying dimension-specific weights (learned with the aid of empirical priors derived from pre-categorical comparisons) to more primitive features of objects. The resulting magnitude distributions, formed and maintained in working memory, are sensitive to contextual influences such as the range of stimuli and polarity of the question. By incorporating psychological reference points that control the precision of magnitudes in working memory and applying the tools of signal detection theory, BARTlet is able to account for a wide range of empirical phenomena involving magnitude comparisons, including the symbolic distance effect and the semantic congruity effect. We discuss the role of reference points in cognitive and social decision-making, and implications for the evolution of relational representations.