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The Problem of Concepts Structure in the Conceptual Spaces Framework

Summary/Abstract: One of the main aims of Peter Gärdenfors’ theory of conceptual spaces is to provide, by means of the geometric methods of representation, a formal model for the prototype structure of concepts. However, his model is not free of theoretical problems regarding an adequate description of the psychologically correct structure of concepts. Therefore, the main purpose of this paper is to raise several questions concerning the relationship between the typicality function and the membership function, as well as to propose some solutions to these problems by offering a model that binds both functions formally. Thus, the proposed model is intended to complement Gärdenfors’ conceptual spaces theory, in which the proper shape of both functions has not been sufficiently problematized. The second aim of the paper is to propose a new approach to vagueness, which is coherent with the formal requirements of the conceptual spaces framework, and at the same time is in line with the solution proposed in the first part of the text.

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