Some representation problems for semiorders

Suppose we have a number representation of a semiorder 〈A, P〉 such that aPb iff f(a)+δ(a) < f(b), for all a, b ∈ A, where δ is a nonnegative function describing the variable jnd. Such an f (here called a closed representation) may not preserve the simple order relation $\text{R}{}^1$ generated by 〈A, P〉, i.e., $\text{aR}{}^1\text{b}$ but f(a) > f(b) for some f, δ and a, b ∈ A. We show that this “paradox” can be eliminated for closed and closed interval representations. For interval representations it appears to be impossible. That is why we introduce a new type of representation (an R-representation) which is of the most general form for number representations that preserve the linear structure of the represented semiorders. The necessary and sufficient condition for an R-representation is given. We also give some independent results on the semiorder structure. Theorems are proved for semiorders of arbitrary cardinality. The Axiom of Choice is used in the proofs.     

Representation of finitely additive semiordered qualitative probability structures

Given a finite Boolean algebra together with a binary relation, necessary and sufficient conditions are given for the existence of a probability measure on the algebra and a real number (the so-called jnd) such that for any two Boolean elements the relation holds if and only if the corresponding probability values of the elements satisfy the threshold inequality (the difference of the probabilities is greater than the jnd).     

The effect of adaptation on taste jnds

The jnd for 0.1 M NaCl was measured under two different adapting conditions. Following adaptation to HOH the jnd was 0.009 M and after 0.1 M adaptation it was .018 M. The implications of this change in sensitivity with differing adaptation for Beidler’s theory are discussed.     

Integration processes during frequency graph comprehension: Performance and eye movements while processing tree maps versus pie charts

Frequency graph types differ in the way how data are translated into visual representations. We compared 2 visualization methods, a traditional circular representation (pie chart) and a rectangular representation (constant column width tree map), which were hypothesized to differ regarding the cognitive ease of visual comparison processes. Performance was evaluated in tasks involving proportion and comparison judgments under both highly controlled and more realistic circumstances. The results showed performance benefits (in terms of reduced response times or error rates) for rectangular representations. Additional eye movement analyses revealed that this benefit was mainly due to a facilitation of scanning the graph for relevant information. The results suggest that facilitating comparison processes by representing the critical variable in less complex visual dimensions (i.e., straight length with constant orientation instead of surface area or curved length) eventually enhances the efficiency of integration processes during graph comprehension.     

3~5岁儿童理解和使用空间表征的特点

以96名3~5儿童为被试,采用自编的儿童空间表征实验任务,在语言表征、模型表征和图画表征三种空间表征形式上,考察了儿童理解和使用空间表征的发展特点。结果表明:(1)总体上,3~5岁儿童理解空间表征的发展水平均显著高于使用空间表征的发展水平。(2)3~5岁儿童理解和使用空间表征的发展表现出显著的年龄效应。(3)从不同的空间表证形式来看,3岁儿童理解语言表征的能力与理解模型表征的能力之间差异显著,4岁儿童使用语言表征的能力与使用模型表征的能力之间的差异、使用语言表征的能力与使用图画表征的能力之间的差异、以及使用模型表征的能力与使用图画表征的能力之间的差异都显著,其余形式的空间表征理解之间的差异或空间表征使用之间的差异在各年龄段中均不显著。     

Intention and Motor Representation in Purposive Action

Are there distinct roles for intention and motor representation in explaining the purposiveness of action? Standard accounts of action assign a role to intention but are silent on motor representation. The temptation is to suppose that nothing need be said here because motor representation is either only an enabling condition for purposive action or else merely a variety of intention. This paper provides reasons for resisting that temptation. Some motor representations, like intentions, coordinate actions in virtue of representing outcomes; but, unlike intentions, motor representations cannot feature as premises or conclusions in practical reasoning. This implies that motor representation has a distinctive role in explaining the purposiveness of action. It also gives rise to a problem: were the roles of intention and motor representation entirely independent, this would impair effective action. It is therefore necessary to explain how intentions interlock with motor representations. The solution, we argue, is to recognise that the contents of intentions can be partially determined by the contents of motor representations. Understanding this content‐determining relation enables better understanding how intentions relate to actions.     

The psychological reality of practical representation

ABSTRACT

We represent the world in a variety of ways: through percepts, concepts, propositional attitudes, words, numerals, recordings, musical scores, photographs, diagrams, mimetic paintings, etc. Some of these representations are mental. It is customary for philosophers to distinguish two main kinds of mental representations: perceptual representation (e.g., vision, auditory, tactile) and conceptual representation. This essay presupposes a version of this dichotomy and explores the way in which a further kind of representation – procedural representation – represents. It is argued that, in some important respects, procedural representations represent differently from both purely conceptual representations and purely perceptual representations. Although procedural representations, just like conceptual and perceptual representations, involve modes of presentation, their modes of presentation are distinctively practical, in a sense which I will clarify. It is argued that an understanding of this sort of practical representation has important consequences for the debate on the nature of know-how.     

两种数量表征系统

数量表征是人类数学能力的基础,数量表征研究中的一个争论焦点在于是否存在两种不同的数量表征系统：对小数的精确表征系统和对大数的近似表征系统。通过综述不同研究领域对数量表征的研究,总结了支持两种表征系统分离的证据：对1~3范围内小数的表征受数量大小的限制,基于指向物体本身的注意,更依赖于物体的知觉特征,对物体及其数量进行精确表征;而对4以上的数量的近似表征系统则受韦伯定律的限制,基于指向数量的模拟幅度的表征,而不依赖单个物体的知觉特征,是对数量的近似的、心理的表征。fMRI、PET和ERP的脑成像研究结果迄今尚无定论,但认知神经科学研究的深入开展将最终阐明数量表征的机制     

内隐学习中表征与意识的关系

近年来研究者分别从表征的质量和表征的外显等级两个方面探讨了内隐学习中表征与意识的关系。有关表征质量与意识的研究,清晰地揭示了影响表征进入意识的因素;而有关表征外显等级与意识的研究,则明确地阐明了什么样的表征才是有意识的。但表征与意识的关系是一个十分复杂的问题,目前仍存在着很大的争议,还有待于进一步的探讨     

Representation at different levels in a conceptual hierarchy

The present study examines the influence of hierarchical level on category representation. Three computational models of representation – an exemplar model, a prototype model and an ideal representation model – were evaluated in their ability to account for the typicality gradient of categories at two hierarchical levels in the conceptual domain of clothes. The domain contains 20 subordinate categories (e.g., trousers, stockings and underwear) and an encompassing superordinate category (CLOTHES). The models were evaluated both in terms of their ability to fit the empirical data and their generalizability through marginal likelihood. The hierarchical level was found to clearly influence the type of representation: For concepts at the subordinate level, exemplar representations were supported. At the superordinate level, however, an ideal representation was overwhelmingly preferred over exemplar and prototype representations. This finding contributes to the increasingly dominant view that the human conceptual apparatus adopts both exemplar representations and more abstract representations, contradicting unitary approaches to categorization.     

Visual mental representations supporting object drawing: How naming a novel object with a novel count noun impacts on young children's object drawing

Object drawing can be supported by a number of cognitive resources, each making available visual information about the object being drawn. These resources include perceptual input, short-term visual memory, and long-term visual memory. Each of these resources has the potential to make available distinct forms of visual representation, including viewpoint-specific and viewpoint-independent representations, object-specific and category representations, and separate representations of object colour. We review neuropsychological and developmental evidence supporting these claims, including evidence that the same drawing can reflect the influence of multiple forms of visual representation. Seven experiments are then reported, investigating object drawing by 4- to 6-year-old children, to confirm the support for drawing provided by different forms of visual representation. Young children are selected for investigation because their drawing is relatively unconstrained by culturally determined norms which, in our culture, dictate that objects should be drawn just as they appear from the vantage point of the drawer. To distinguish the support provided by object and category representations, the experiments exploit the privileged links between count nouns as object labels, and representations of object categories. In addition, pre-established representations, visual or otherwise, are precluded from influencing drawing by asking the children to draw novel objects, and by creating novel count nouns with which to label the objects. The results reveal how viewpoint-specific perceptual representations, object-specific representations of shape and of colour, and category representations of shape can each impact on object drawing, and in some circumstances on the same drawing. It appears that simple drawing tasks have the potential to reveal some of the distinct types of representation able to support visual cognition.     

Shared Knowledge Matters: Culture as Intersubjective Representations

The intersubjective representation approach to culture focuses on cultural members’ shared knowledge representations about the culture that they are in. Members of the same culture tend to share certain knowledge representations of the central characteristics of the culture. These shared cultural representations are established and perpetuated through dynamic communicative processes. Recent empirical research has provided support for the incremental value of intersubjective cultural representations in research on cultural identity, social cognition, and behaviors. The intersubjective representation approach complements extant research on culture as self and external artifacts. In doing so, it allows for a more comprehensive understanding of culture’s role in social and personality psychological processes.     

Ordinal network representation: Representing proximities by graphs

Ordinal network representations are graph-theoretic representations of proximity data. They seek to provide parsimonious representations of the ordinal (nonmetric) information in observed proximity data by means of the minimum-path-length distance of a connected and weighted graph. In contrast to traditional tree-based graph-theoretic approaches, ordinal network representation is not limited to but includes the representation by trees. Asymmetry in the proximity data and violations of zero-minimality are allowed for. The paper explores fundamental representation and uniqueness results and discusses a method of constructing ordinal network representations. A simple strategy for handling the problem of errors in the data is described and illustrated.This work was supported by grant Fe 75/20-2 of the Deutsche Forschungsgemeinschaft. The author is indebted to Hubert Feger for many inspiring discussions.     

The development of numerical estimation: evidence for multiple representations of numerical quantity

Abstract - We examined children's and adults' numerical estimation and the representations that gave rise to their estimates. The results were inconsistent with two prominent models of numerical representation: the logarithmic-ruler model, which proposes that people of all ages possess a single, logarithmically spaced representation of numbers, and the accumulator model, which proposes that people of all ages represent numbers as linearly increasing magnitudes with scalar variability. Instead, the data indicated that individual children possess multiple numerical representations; that with increasing age and numerical experience, they rely on appropriate representations increasingly often; and that the numerical context influences their choice of representation. The results, obtained with second graders, fourth graders, sixth graders, and adults who performed two estimation tasks in two numerical contexts, strongly suggest that one cause of children's difficulties with estimation is reliance on logarithmic representations of numerical magnitudes in situations in which accurate estimation requires reliance on linear representations.     

多元表征假设：概念表征机制的新观点

传统的认知主义认为概念表征是与主体的感知系统无关的抽象符号。而具身理论则认为,概念表征以主体的感觉、知觉运动系统为基础的,感知系统在概念表征中具有中心作用。然而,具身性假设无法恰当的解释抽象概念表征这一问题。这种局限性说明主体的概念系统可能具有多元表征机制：既包括感知表征以加工与身体经验相关的具体知识,也包括抽象符号表征以加工与身体经验无关的抽象知识。来自病理学、认知神经科学和行为实验的实证研究证明了不同类型的概念会涉及不同的表征机制,证实了多元表征存在的合理性。今后的研究应探讨各种表征机制之间的关系等问题。     

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.     

Searching while loaded: Visual working memory does not interfere with hybrid search efficiency but hybrid search uses working memory capacity

In “hybrid search” tasks, such as finding items on a grocery list, one must search the scene for targets while also searching the list in memory. How is the representation of a visual item compared with the representations of items in the memory set? Predominant theories would propose a role for visual working memory (VWM) either as the site of the comparison or as a conduit between visual and memory systems. In seven experiments, we loaded VWM in different ways and found little or no effect on hybrid search performance. However, the presence of a hybrid search task did reduce the measured capacity of VWM by a constant amount regardless of the size of the memory or visual sets. These data are broadly consistent with an account in which VWM must dedicate a fixed amount of its capacity to passing visual representations to long-term memory for comparison to the items in the memory set. The data cast doubt on models in which the search template resides in VWM or where memory set item representations are moved from LTM through VWM to earlier areas for comparison to visual items.     

Social representations and intergroup conflicts: Who's smoking here?

We studied the influence of explicitating a social conflict between smokers and nonsmokers on the social representations held about tobacco. Two representations were found: a psychological' representation which was defined by psychological explanations of the causes of beginning to smoke, a characterization of smokers as psychologically disturbed, and negative feelings towards smokers; a second defensive representation which attributes smoking to social factors, and hold both a positive stereotype of smokers and positive feelings towards smokers. The percentage of smokers who adhere to the defensive representation increased significantly when the conflict was made salient. Non-smokers were not influenced by the explicitation of the social conflict. The structure of each representation was analyzed. It was found that in the psychological' representation the structuring element was the negative stereotype of smokers. By contrast, the structuring element in the defensive representation was identification with smokers. The implicatlons of this data for theories of both intergroup relations and social representations are discussed.     

Scaling of saturation and hue

The study concerns the relation of saturation to the purity and luminance of aperture colors viewed in a dark surround. For the primary hues, red, yellow, green, and blue, and the intermediate hues, orange and yellowish green, the saturations increased as power functions of colorimetric purity. An IS-dB increase in luminance caused a threefold increase in the exponent for yellow, but luminance had little effect on the exponents of the other colors. The direct heterochromatic matching of saturation to saturation confirmed the validity of the scales determined by magnitude estimation and led to the construction of families of saturation scales based on a common unit called a crome. Equisection and jnd scales were also determined. Their nonlinearity suggests that saturation is a prothetic continuum. It was found that mixing red or green with yellow behaves much the same as mixing red or green with achromatic light. The changes in hue behave as prothetic continua, for the equisection and jnd scales are nonlinearly related to the power-function scales obtained by magnitude estimation and matching.