Parameterised frames and conceptual spaces

该项目源于杜塞尔多夫991合作研究单位的D 01项目，其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。在后一个项目中，研究重点是原型概念及其在常识推理中的作用的调查。为了这个目的，我们开发了一个概念的原型框架，不仅包括一般的属性值结构的框架，但进行数值信息的概率或典型性的值和诊断的属性。携带数值信息的框架被称为“参数化框架”。 与简单的特征表相比，框架的认知优势在于为复杂的语义结构提供了经济且易于理解的表征。表示复杂概念，特别是原型概念的另一种方法是概念空间建模。概念空间和框架共享一个功能结构。两者都基于属性，即，将值空间瓦尔中的值赋给给定对象a的函数X：X（a）∈瓦尔。例如，属性colour在值空间瓦尔= {red，绿色，.}中分配值。对于一个给定的对象：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，这在概念空间中是找不到的。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。 这两种方法的优点和缺点是什么？特别是，在何种程度上，我们的框架帐户可以受益于概念空间的几何结构？这些问题激发了这个项目的主要目标，可以总结如下：目标1 -提供概念空间和框架的比较，特别是参数化框架。目的2 -在参数化框架中嵌入概念空间结构。几何工具是卓有成效地应用在参数化框架，而不损害一般的框架建模（特别是，他们的递归结构）。目的3 -调查的本体论和认知的自然性框架及其属性概念，通过应用标准的自然性概念空间理论，如凸性。据证实，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.