Boundary conditions of conceptual spaces

概念知识表征的拓扑结构仍然存在着激烈的争论。可以区分两个主要账户：空间账户和非空间账户。试图在这些帐户之间进行裁决的努力没有成功。我们假设，在收购和性能的边界条件决定的地形结构在认知和神经水平。这个建议的目的是划定边界条件，界定地形的概念知识。将解决两个主要问题：1。语境因素对概念知识的结构及其行为和神经表达有何影响？例如，数的传递性质使其本身适合于将数值大小空间投影到一维流形上。对于更复杂（例如，二维）的概念，表示可以采用类似地图的拓扑。然而，对于非传递序列和其他记忆内容（如算术事实），空间架构似乎不太适合，并且已经提出了类似图形的语义网络。因此，概念知识的传递性和维度性可能需要不同的拓扑结构，因此可能代表定义拓扑结构的潜在边界因素。其他未解决的问题，将解决包括两个以前不相关的传递系列如何投射到一个共同的度量标准，以及如何二维概念空间转化为手动和视觉行为的问题。其他潜在的边界因素，如专业知识和对概念的熟悉程度，在概念表征的构建中扮演什么角色？新获得的概念与现有知识联系的方式影响行为。我们研究了儿童在数字符号习得过程中，先天数字量表征的特征效应（距离效应和大小效应）是如何产生的。因此，我们调查的影响，发展的依赖关系的形状的概念knowledge.Using一组共同的实验，该项目结合了互补的行为措施，描绘地形结构（反应时间，在触摸屏上的指向位置，眼睛跟踪的参数）和神经功能的功能磁共振成像数据从成人和小学生。为了阐明先前存在的知识的作用，该项目结合了一种培训方法，在这种方法中，参与者将被教导新的概念空间，并对现有的概念进行调查，如数字知识。描述获得和适应概念内容的神经和认知原则将促进我们对概念知识表征的理解。通过将焦点从是否所有概念都在空间上表示的问题转移到上下文变量如何塑造观察到的表现这一更富有成效的问题，该项目实现了更富有成效的辩论。

The topographic structure underlying conceptual knowledge representations remains vividly debated. Two major accounts can be distinguished: spatial vs. non-spatial accounts. Attempts to adjudicate between these accounts have been unsuccessful. We hypothesize that boundary conditions during acquisition and performance determine the topographic structure at the cognitive and neural level. This proposal aims at delineating the boundary conditions that define the topography of conceptual knowledge. Two major questions will be addressed:1. What is the impact of context factors on the architecture of conceptual knowledge and its behavioral and neural expression? The transitive nature of numbers, for example, lends itself for spatially projecting numerical magnitude onto a one-dimensional manifold. For more complex (e.g. two-dimensional) concepts, the representation may take a map-like topography. For non-transitive series and other memory contents such as arithmetic facts, however, a spatial architecture appears less suited and graph-like, semantic networks have been proposed. Hence, transitivity and dimensionality of the conceptual knowledge may call for different topographies and may hence represent potential boundary factors that define the topography. Other unresolved issues that will be addressed include the question how two previously unrelated transitive series are projected onto a common metric and how two-dimensional conceptual spaces translate into manual and ocular behavior.2. What role do other potential boundary factors such as expertise and familiarity with concepts play in the construction of conceptual representations? The way in which newly acquired concepts are linked with existing knowledge influences behavior. We investigate how signature effects of the innate numerical magnitude representation (distance and size effects) emerge during the acquisition of numerical symbols in children. Hence we investigate the impact of developmental dependencies on the shape of conceptual knowledge.Using a common set of experiments, the project combines complementary behavioral measures to delineate the topographical structure (reaction times, pointing positions on a touchscreen, ocular parameters from eye tracking) and neurofunctional functional magnetic resonance imaging data from adults and elementary school children. To elucidate the role of pre-existing knowledge, the project combines a training approach in which participants will be taught new conceptual spaces with the investigation of existing concepts such as number knowledge.Delineating neural and cognitive principles underlying the acquisition and adaptation of conceptual content will advance our understanding of conceptual knowledge representation. By shifting the focus from the question whether all concepts are spatially represented toward the more fruitful question of how contextual variables shape the observed performance, this project enables a more productive debate.