Parameterised frames and conceptual spaces

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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.