The effect of external representations on numeric tasks

This article explores the effect of external representations on numeric tasks. Through several minor modifications on the previously reported two-digit number comparison task, we obtained different results. Rather than holistic comparison, we found parallel comparison. We argue that this difference was a reflection of different representational forms: The comparison was based on internal representations in previous studies but on external representations in our present study. This representational effect is discussed under a framework of distributed number representations. We propose that in numerical tasks involving external representations, numbers should be considered as distributed representations, and the behaviour in these tasks should be considered as the interactive processing of internal and external information through the interplay of perceptual and cognitive processes. We suggest that theories of number representations and process models of numerical cognition should consider external representations as an essential component.     

Aligning Logical and Psychological Contributions to the Understanding of Human Reasoning

Modern logic is an abstract study of consequence rather than a mechanistic study of reasoning. This abstract view has much to offer psychological studies of the representations which implement human reasoning. This paper reviews recent results showing the abstract equivalence of all the main psychological competence models of syllogistic reasoning. Their apparently contrasting representations are computationally equivalent for the kind of data presented. The true empirical contrasts between theories lie in other details of implementation — in whether integrated representations are constructed and in the sequence of cases considered. These contrasts are independent of sentential, graphical or mental model representation.Logic is also a guide to representation requirements. Linear syllogism models are representable by sequences of tokens, whereas categorial syllogism models generally require attribute binding. However, one consequence of the present semantic analysis is that all categorial syllogism competence models converge on an algorithm which avoids representation of more than a single sequence.The paper goes on to consider what evidence could distinguish the representations implementing reasoning in working memory. The example of dual task paradigms is considered and some conceptual questions are raised about the identification of the modalities of working memory subsystems with linguistic and spatial representations. Carefully distinguishing memory medium from memory interpretation leads to the conclusion that it is the interpretation of the contents of memory which determines whether it holds spatial or linguistic information. It is argued that the critical dimension for understanding reasoning processes is the expressiveness of interpretation of representations.     

Building Cognition: The Construction of Computational Representations for Scientific Discovery

Novel computational representations, such as simulation models of complex systems and video games for scientific discovery (Foldit, EteRNA etc.), are dramatically changing the way discoveries emerge in science and engineering. The cognitive roles played by such computational representations in discovery are not well understood. We present a theoretical analysis of the cognitive roles such representations play, based on an ethnographic study of the building of computational models in a systems biology laboratory. Specifically, we focus on a case of model‐building by an engineer that led to a remarkable discovery in basic bioscience. Accounting for such discoveries requires a distributed cognition (DC) analysis, as DC focuses on the roles played by external representations in cognitive processes. However, DC analyses by and large have not examined scientific discovery, and they mostly focus on memory offloading, particularly how the use of existing external representations changes the nature of cognitive tasks. In contrast, we study discovery processes and argue that discoveries emerge from the processes of building the computational representation. The building process integrates manipulations in imagination and in the representation, creating a coupled cognitive system of model and modeler, where the model is incorporated into the modeler's imagination. This account extends DC significantly, and we present some of the theoretical and application implications of this extended account.     

Theory learning as stochastic search in the language of thought

We present an algorithmic model for the development of children's intuitive theories within a hierarchical Bayesian framework, where theories are described as sets of logical laws generated by a probabilistic context-free grammar. We contrast our approach with connectionist and other emergentist approaches to modeling cognitive development. While their subsymbolic representations provide a smooth error surface that supports efficient gradient-based learning, our symbolic representations are better suited to capturing children's intuitive theories but give rise to a harder learning problem, which can only be solved by exploratory search. Our algorithm attempts to discover the theory that best explains a set of observed data by performing stochastic search at two levels of abstraction: an outer loop in the space of theories and an inner loop in the space of explanations or models generated by each theory given a particular dataset. We show that this stochastic search is capable of learning appropriate theories in several everyday domains and discuss its dynamics in the context of empirical studies of children's learning.     

Directions in Connectionist Research: Tractable Computations Without Syntactically Structured Representations

Should connectionists abandon the quest for tractably computable cognitive transition functions while retaining syntactically structured mental representations? We argue, in opposition to Horgan, that it should not. We argue that the case against tractably computable functions, based upon the claimed isotropic and Quinean character of cognition, fails since cognition is not as isotropic and Quinean as Fodor and Horgan contend. Moreover, we illustrate how current research in both connectionism and cognitive neuroscience suggests that tractability can be preserved through division of overall computations into modular sub-processes, each of which is tractable. As to syntactically structured representations, we argue that they are unneeded for most cognitive tasks organisms confront, and that when they are needed, they may be provided by external representational media such as natural language. Moreover, we note that increasingly cognitive linguistics has become the ally of connectionism and that the research program of cognitive linguistics suggests that abilities to use natural languages may be developed without requiring syntactically structured mental representations to exist prior to natural language.     

Constructing Semantic Models From Words,Images, and Emojis

A number of recent models of semantics combine linguistic information, derived from text corpora, and visual information, derived from image collections, demonstrating that the resulting multimodal models are better than either of their unimodal counterparts, in accounting for behavioral data. Empirical work on semantic processing has shown that emotion also plays an important role especially in abstract concepts; however, models integrating emotion along with linguistic and visual information are lacking. Here, we first improve on visual and affective representations, derived from state-of-the-art existing models, by choosing models that best fit available human semantic data and extending the number of concepts they cover. Crucially then, we assess whether adding affective representations (obtained from a neural network model designed to predict emojis from co-occurring text) improves the model's ability to fit semantic similarity/relatedness judgments from a purely linguistic and linguistic–visual model. We find that, given specific weights assigned to the models, adding both visual and affective representations improves performance, with visual representations providing an improvement especially for more concrete words, and affective representations improving especially the fit for more abstract words.     

Visual and Affective Multimodal Models of Word Meaning in Language and Mind

One of the main limitations of natural language-based approaches to meaning is that they do not incorporate multimodal representations the way humans do. In this study, we evaluate how well different kinds of models account for people's representations of both concrete and abstract concepts. The models we compare include unimodal distributional linguistic models as well as multimodal models which combine linguistic with perceptual or affective information. There are two types of linguistic models: those based on text corpora and those derived from word association data. We present two new studies and a reanalysis of a series of previous studies. The studies demonstrate that both visual and affective multimodal models better capture behavior that reflects human representations than unimodal linguistic models. The size of the multimodal advantage depends on the nature of semantic representations involved, and it is especially pronounced for basic-level concepts that belong to the same superordinate category. Additional visual and affective features improve the accuracy of linguistic models based on text corpora more than those based on word associations; this suggests systematic qualitative differences between what information is encoded in natural language versus what information is reflected in word associations. Altogether, our work presents new evidence that multimodal information is important for capturing both abstract and concrete words and that fully representing word meaning requires more than purely linguistic information. Implications for both embodied and distributional views of semantic representation are discussed.     

Working memory and number line representations in single-digit addition: Approximate versus exact,nonsymbolic versus symbolic

How do kindergarteners solve different single-digit addition problem formats? We administered problems that differed solely on the basis of two dimensions: response type (approximate or exact), and stimulus type (nonsymbolic, i.e., dots, or symbolic, i.e., Arabic numbers). We examined how performance differs across these dimensions, and which cognitive mechanism (mental model, transcoding, or phonological storage) underlies performance in each problem format with respect to working memory (WM) resources and mental number line representations. As expected, nonsymbolic problem formats were easier than symbolic ones. The visuospatial sketchpad was the primary predictor of nonsymbolic addition. Symbolic problem formats were harder because they either required the storage and manipulation of quantitative symbols phonologically or taxed more WM resources than their nonsymbolic counterparts. In symbolic addition, WM and mental number line results showed that when an approximate response was needed, children transcoded the information to the nonsymbolic code. When an exact response was needed, however, they phonologically stored numerical information in the symbolic code. Lastly, we found that more accurate symbolic mental number line representations were related to better performance in exact addition problem formats, not the approximate ones. This study extends our understanding of the cognitive processes underlying children's simple addition skills.     

Does linguistic reversibility exist? an experimental exploration of a psycholinguistic construct

Three experiments were devised involving 176 subjects aged between 5-0 and 8-1 years to examine children's receptive control of a set of four intersentence relations (identity, antonymy, structure reversal, equivalence) and to relate this linguistic ability to levels of cognitive functioning as assessed by the Piagetian measureDeux Sens de l'Orientation. The results indicate a significant but moderate correlation between performance on the two tasks. Cognitive precedence with respect to corresponding linguistic ability was observed in only one of the experiments, where linguistic performance was unsually low due to phonological interference between the lexical items used. The results were interpreted as giving evidence of linguistic reversibility—partially independent from cognitive reversibility though isomorphic with it—in the perceptual-figurative mode, resulting in flexible and efficient processing of linguistic inversions and even converse relations by preoperational children. These data complement previous psycholinguistic research in the Piagetian tradition, which had shown cognitive precedence relative to corresponding linguistic processes. It is suggested that previous research had tapped mainly linguistic processes in the cognitive operational mode, and that future research needs to examine the interrelation between the two modes.     

Representing Spatial Structure Through Maps and Language: Lord of the Rings Encodes the Spatial Structure of Middle Earth

Spatial mental representations can be derived from linguistic and non‐linguistic sources of information. This study tested whether these representations could be formed from statistical linguistic frequencies of city names, and to what extent participants differed in their performance when they estimated spatial locations from language or maps. In a computational linguistic study, we demonstrated that co‐occurrences of cities in Tolkien’s Lord of the Rings trilogy and The Hobbit predicted the authentic longitude and latitude of those cities in Middle Earth. In a human study, we showed that human spatial estimates of the location of cities were very similar regardless of whether participants read Tolkien’s texts or memorized a map of Middle Earth. However, text‐based location estimates obtained from statistical linguistic frequencies better predicted the human text‐based estimates than the human map‐based estimates. These findings suggest that language encodes spatial structure of cities, and that human cognitive map representations can come from implicit statistical linguistic patterns, from explicit non‐linguistic perceptual information, or from both.     

The role of corpus size and syntax in deriving lexico-semantic representations for a wide range of concepts

One of the most significant recent advances in the study of semantic processing is the advent of models based on text and other corpora. In this study, we address what impact both the quantitative and qualitative properties of corpora have on mental representations derived from them. More precisely, we evaluate models with different linguistic and mental constraints on their ability to predict semantic relatedness between items from a vast range of domains and categories. We find that a model based on syntactic dependency relations captures significantly less of the variability for all kinds of words, regardless of the semantic relation between them or their abstractness. The largest difference was found for concrete nouns, which are commonly used to assess semantic processing. For both models we find that limited amounts of data suffice in order to obtain reliable predictions. Together, these findings suggest new constraints for the construction of mental models from corpora, both in terms of the corpus size and in terms of the linguistic properties that contribute to mental representations.     

Do First Graders Make Efficient Use of External Number Representations? The Case of the Twenty-Frame

External number representations are commonly used throughout the first years of instruction. The twenty-frame is a grid that contains two rows of 10 dots each, and within each row, dots are organized in two groups of five. The assumption is that children can make use of these structures for enumerating the dots, rather than relying on one-by-one counting. We compared first-grade children's performance on two types of computerized enumeration tasks, in which between one and 20 dots were presented in random arrangements or on a twenty-frame. The number of dots was a strong predictor of response times and accuracy rates in the enumeration task with random arrangements but not in the twenty-frame task. Performance on the twenty-frame task was correlated with performance on a number and arithmetic test, even when other cognitive variables were statistically controlled. We discuss these findings in the light of theories on utilizing external representations to support numerical learning.     

Representations gone mental

Many philosophers and psychologists have attempted to elucidate the nature of mental representation by appealing to notions like isomorphism or abstract structural resemblance. The ‘structural representations’ that these theorists champion are said to count as representations by virtue of functioning as internal models of distal systems. In his 2007 book, Representation Reconsidered, William Ramsey endorses the structural conception of mental representation, but uses it to develop a novel argument against representationalism, the widespread view that cognition essentially involves the manipulation of mental representations. Ramsey argues that although theories within the ‘classical’ tradition of cognitive science once posited structural representations, these theories are being superseded by newer theories, within the tradition of connectionism and cognitive neuroscience, which rarely if ever appeal to structural representations. Instead, these theories seem to be explaining cognition by invoking so-called ‘receptor representations’, which, Ramsey claims, aren’t genuine representations at all—despite being called representations, these mechanisms function more as triggers or causal relays than as genuine stand-ins for distal systems. I argue that when the notions of structural and receptor representation are properly explicated, there turns out to be no distinction between them. There only appears to be a distinction between receptor and structural representations because the latter are tacitly conflated with the ‘mental models’ ostensibly involved in offline cognitive processes such as episodic memory and mental imagery. While structural representations might count as genuine representations, they aren’t distinctively mental representations, for they can be found in all sorts of non-intentional systems such as plants. Thus to explain the kinds of offline cognitive capacities that have motivated talk of mental models, we must develop richer conceptions of mental representation than those provided by the notions of structural and receptor representation.     

认知地图技术及其在管理心理学中的应用述评

认知地图技术是用来获取个体对某个特定领域独特理解的图形化描述的一系列方法的总称,包括认知诱发技术与分析技术.在详细阐述其概念、原理的基础上,本文结合一个共享心智模型的研究实例,展示了认知地图技术应用的一般步骤.然后,介绍了认知地图技术在管理心理学中的应用.并针对认知地图技术存在的问题,对未来的研究进行了展望,即从认知地图技术的理论、应用及软件等方面开展深入研究.     

Time in the mind: using space to think about time

How do we construct abstract ideas like justice, mathematics, or time-travel? In this paper we investigate whether mental representations that result from physical experience underlie people's more abstract mental representations, using the domains of space and time as a testbed. People often talk about time using spatial language (e.g., a long vacation, a short concert). Do people also think about time using spatial representations, even when they are not using language? Results of six psychophysical experiments revealed that people are unable to ignore irrelevant spatial information when making judgments about duration, but not the converse. This pattern, which is predicted by the asymmetry between space and time in linguistic metaphors, was demonstrated here in tasks that do not involve any linguistic stimuli or responses. These findings provide evidence that the metaphorical relationship between space and time observed in language also exists in our more basic representations of distance and duration. Results suggest that our mental representations of things we can never see or touch may be built, in part, out of representations of physical experiences in perception and motor action.     

Reasoning bias for the recall of one's own beliefs in a Smarties task for adults

While many studies in the theory of mind (ToM) literature have investigated how we understand others' mental states, few have explored the mechanism by which we reflect on our own mental states. This study examined how adults reflect on their own and others' mental states within the same ToM task. To do so, we modified the Smarties task, one of the traditional ToM tasks for children. The results showed that adult participants were biased by outcome knowledge when recalling their false belief and that the participants who overestimated their false belief also overestimated the mental states of a naive other. These results were analogous to young children's failure in the Smarties task. Considering the current findings, we discuss possible cognitive processes that are common across children and adults when reflecting on their own mental states and the mental states of others.     

Reducing the Linear Perception of Nonlinearity: Use of a Physical Representation

Research shows that while judging accumulations of quantities over time (e.g., money in a bank account or CO₂ in Earth's atmosphere), people assume that the shape of the accumulation is similar to the shape of the inflow (i.e., people rely on a correlation heuristic). Relying on the correlation heuristic is particularly worrisome for Earth's climate, as judging the CO₂ accumulation according to its emissions (inflow) would underestimate the actual (nonlinear) increase. This misperception undermines the seriousness of climate problem and results in wait‐and‐see behavior. We report two experiments where the effectiveness of a physical representation is compared with graphical and text representations in reducing people's underestimation of nonlinear accumulation in different contexts and problems. A physical representation presents an accumulation using a picture that works as a metaphor. In the first experiment, participants drew the shape of an accumulation over time relying on physical or graphical representations in one of two contexts: carbon dioxide and marbles. Although the participants underestimated the accumulation in both contexts, underestimations were reduced in the physical representation compared with the graphical representation. In the second experiment, we extended the evaluation of physical representations against both text and graphical representations in two different climate problems (with linearly increasing or decreasing inflow). Again, underestimations of the accumulation were reduced in the physical representation compared with the other two representations, regardless of the nature of the problem. We discuss implications of using the physical representation for improving people's estimates of nonlinear CO₂ accumulation. Copyright © 2011 John Wiley & Sons, Ltd.     

Exemplars, prototypes, similarities, and rules in category representation: an example of hierarchical bayesian analysis

This article demonstrates the potential of using hierarchical Bayesian methods to relate models and data in the cognitive sciences. This is done using a worked example that considers an existing model of category representation, the Varying Abstraction Model (VAM), which attempts to infer the representations people use from their behavior in category learning tasks. The VAM allows for a wide variety of category representations to be inferred, but this article shows how a hierarchical Bayesian analysis can provide a unifying explanation of the representational possibilities using 2 parameters. One parameter controls the emphasis on abstraction in category representations, and the other controls the emphasis on similarity. Using 30 previously published data sets, this work shows how inferences about these parameters, and about the category representations they generate, can be used to evaluate data in terms of the ongoing exemplar versus prototype and similarity versus rules debates in the literature. Using this concrete example, this article emphasizes the advantages of hierarchical Bayesian models in converting model selection problems to parameter estimation problems, and providing one way of specifying theoretically based priors for competing models.     

Representations and Cognitive Explanations: Assessing the Dynamicist's Challenge in Cognitive Science

Advocates of dynamical systems theory (DST) sometimes employ revolutionary rhetoric. In an attempt to clarify how DST models differ from others in cognitive science, I focus on two issues raised by DST: the role for representations in mental models and the conception of explanation invoked. Two features of representations are their role in standing-in for features external to the system and their format. DST advocates sometimes claim to have repudiated the need for stand-ins in DST models, but I argue that they are mistaken. Nonetheless, DST does offer new ideas as to the format of representations employed in cognitive systems. With respect to explanation, I argue that some DST models are better seen as conforming to the covering-law conception of explanation than to the mechanistic conception of explanation implicit in most cognitive science research. But even here, I argue, DST models are a valuable complement to more mechanistic cognitive explanations.