# Conceptual Spaces

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The theory also puts forward the notion that natural categories are convex regions in a conceptual spaces. In that if ${\displaystyle x}$ and ${\displaystyle y}$ are elements of a category, and if ${\displaystyle z}$ is between ${\displaystyle x}$ and ${\displaystyle y}$, then ${\displaystyle z}$ 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.