This paper is devoted to the empirical evaluation of the extension of the Gärdenfors’ similarity model. His proposition insufficiently emphasizes the asymmetry of the modeled relationship of similarity. The proposed modification allows one to include the asymmetry of similarity and significantly sensitize the model to any contextual nuances. The model was compared with other theoretical proposals of geometrical modeling of similarity, including two asymmetric models and one symmetrical. The empirical evaluation of the model took place in two series of experiments. The obtained statistical data were compared with results inferred by tested models. The evaluation was based on iterative procedure designed to minimize the error generated by all compared models.
This paper is devoted to the empirical evaluation of the extension of the Gärdenfors’ similarity model. His proposition insufficiently emphasizes the asymmetry of the modeled relationship of similarity. The proposed modification allows one to include the asymmetry of similarity and significantly sensitize the model to any contextual nuances. The model was compared with other theoretical proposals of geometrical modeling of similarity, including two asymmetric models and one symmetrical. The empirical evaluation of the model took place in two series of experiments. The obtained statistical data were compared with results inferred by tested models. The evaluation was based on iterative procedure designed to minimize the error generated by all compared models.
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.
The concept of similarity is undoubtedly one of the cornerstones of contemporary cognitive science. Although it plays an important role in most of the cognitive activities of man, the issue of the appropriate representation of similarities is an extremely difficult task. One approach to the issue of similarity representation is based on the geometric model used in Gärdenfors’ conceptual spaces theory. However, the criticism of the geometrical model of similarity still seems to remain valid, and the model itself is regarded, by many critics, as an inadequate tool for representing mental phenomena. The primary objective of the article is to propose a model of similarity which would be insensitive to this criticism. The first part is devoted to basic assumptions of the conceptual spaces theory and the axioms of its model of similarity. In the second part I present the most common critical arguments against the geometrical model of similarity and then introduce a geometric model of similarity immune to the criticism.
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