Parameterised frames and conceptual spaces

该项目源于杜塞尔多夫合作研究小组991的D01项目，该项目的研究重点是框架理论及其在语言学、哲学和认知科学中的应用。在第二个项目中，研究集中在原型概念及其在常识推理中的作用。为此，我们提出了原型框架的概念，它不仅包括框架的一般属性值结构，而且携带关于值的概率或典型性以及属性的诊断性的数字信息。携带数字信息的帧被称为“参数化帧”。与简单的特征列表相比，框架的认知优势是提供了对复杂语义结构的经济和易于理解的表示。表示复杂概念，特别是原型概念的另一种方法是通过概念空间建模。概念空间和框架共享一个功能结构。两者都基于属性，即将值空间val中的值分配给给定对象a：x(A)∈val的函数X。例如，属性COLOR将值空间val={red，green，...}中的值分配给给定对象：COLOR(MyShirt)=red。然而，也有显著的差异。一方面，框架由具有递归结构的属性束组成，这是我们在概念空间中找不到的。另一方面，概念空间通过距离度量将值空间与拓扑或几何结构相关联。这两种方法的优缺点是什么？特别是，我们的框架帐户可以在多大程度上受益于概念空间的几何结构？这些问题激发了本项目的主要目标，可概括如下：目标1--提供概念空间和框架的比较，特别是参数化框架。研究它们的共性和差异性、优势和局限性。目的2-将概念空间结构嵌入到参数化框架中。几何工具被有效地应用于参数化框架中，而不会影响一般框架建模(特别是它们的递归结构)。目标3-通过应用概念空间理论中的自然标准，例如凸性，来研究框架及其属性概念的本体论和认知自然性。据推测，框架的自然性与其易学性和认知有用性密切相关。

This project grew out of project D01 of the Düsseldorf Collaborative Research Unit 991, whose focus of research was the theory of frames and their application in linguistics, philosophy and cognitive science. In the latter project, the research focused on the investigation of prototype concepts and their role in common-sense reasoning. For this purpose, we developed a conception of prototype frames that consist not only of the general attribute value structures of frames, but carry numeric information about the probability or typicality of the values and the diagnosticity of the attributes. Frames carrying numerical information are called 'parameterised frames'. The cognitive advantage of frames, as compared to simple feature lists, is to offer economical and easily comprehensible representations of complex semantic structures. An alternative method for representing complex concepts, especially prototype concepts, is the modelling by conceptual spaces. Conceptual spaces and frames share a functional structure. Both are based on attributes, i.e., functions X that assign values out of a value space Val to given objects a: X(a)∈Val. For example, the attribute colour assigns a value in the value space Val = {red, green,...} to a given object: colour(myshirt) = red. However, there are also remarkable differences. Frames, on the one hand, consist of bundles of attributes with a recursive structure, which we do not find in conceptual spaces. Conceptual spaces, on the other hand, associate value spaces with topological or geometric structures by means of a distance measure. What are the advantages and disadvantages of these two approaches? In particular, to what extent can our frame account benefit from the geometrical structures of conceptual spaces? These questions motivate the major aims of this project, that can be summarized as follows:Aim 1 – Providing a comparison of conceptual spaces and frames, especially parameterised frames. Investigating their commonalities and differences, advantages and limitations.Aim 2 – Embedding conceptual space structures in parameterised frames. Geometrical tools are fruitfully applied within parameterised frames without compromising the general frame modelling (in particular, their recursive structure).Aim 3 – Investigating the ontological and cognitive naturalness of frames and their attribute concepts, by applying criteria of naturality from conceptual spaces theory, such as convexity. It is conjectured that naturalness of frames is strongly correlated with the ease of their learnability and their cognitive usefulness.