Hausdorff completion

The Theory of Conceptual Spaces is a theory about concept representation proposed by Peter Gärdenfors. It is motivated by the notions like conceptual similarity and prototype theory. A conceptual space is multi-dimensional feature space where points denote objects, and regions denote concepts. Its bases are composed by quality dimensions, which denote basic features in which concepts and objects can be compared, as such as weight, colour, taste and so on.

The theory also puts forward the notion that natural categories are convex regions in a conceptual spaces. In that if $x$ and $y$ are elements of a category, and if $z$ is between $x$ and $y$, then $z$ is also likely to belong to the category. The notion of concept convexity allow the interpretation of the focal points of regions as category prototypes. In the more general formulations of the theory, concepts are defined in terms conceptual similarity to their prototypes.

See also

• Prototype Theory
• Similarity (psychology)

Notes

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