Formalized Conceptual Spaces with a Geometric Representation of Correlations

Autor(en): Bechberger, L.
Kühnberger, K.-U. 
Erscheinungsdatum: 2019
Herausgeber: Springer Science and Business Media B.V.
Enthalten in: Synthese Library
Band: 405
Startseite: 29
Seitenende: 58
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a similarity space and concepts are represented by convex regions in this space. After pointing out a problem with the convexity requirement, we propose a formalization of conceptual spaces based on fuzzy star-shaped sets. Our formalization uses a parametric definition of concepts and extends the original framework by adding means to represent correlations between different domains in a geometric way. Moreover, we define various operations for our formalization, both for creating new concepts from old ones and for measuring relations between concepts. We present an illustrative toy-example and sketch a research project on concept formation that is based on both our formalization and its implementation. © 2019, Springer Nature Switzerland AG.
ISSN: 01666991
DOI: 10.1007/978-3-030-12800-5_3
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