Conceptual space

The 11 exhaustive topological relations between regions. In Gärdenfors' theory, these relations illustrate how spatial concepts can be represented as geometric structures within a conceptual space.

A conceptual space is a geometric structure that represents a number of quality dimensions, which denote basic features by which concepts and objects can be compared, such as weight, color, taste, temperature, pitch, and the three ordinary spatial dimensions.[1][2]: 4 In a conceptual space, points denote objects, and regions denote concepts. The theory of conceptual spaces is a theory about concept learning first proposed by Peter Gärdenfors.[3][4][5] It is motivated by notions such as conceptual similarity and prototype theory.

The theory also puts forward the notion that natural categories are convex regions in conceptual spaces.[1]: 5 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 allows 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. Conceptual spaces have found applications in both cognitive modelling and artificial intelligence.[1][6]

## See also

* Categorical perception
* Cognitive architecture
* Color space
* Commonsense reasoning
* Conceptual dependency theory
* Distributional semantics
* Face space
* Formal concept analysis
* Frame semantics
* Global workspace theory
* Image schema
* Phonetic space
* Semantic space
* Similarity
* State space
* Vector space model
* Visual space

## Notes

1. ↑ 1.0 1.1 1.2 Zenker, Frank; Gärdenfors, Peter, eds (2015). Applications of conceptual spaces: the case for geometric knowledge representation. Synthese library: studies in epistemology, logic, methodology, and philosophy of science. 359. Cham: Springer-Verlag. ISBN 978-3319150208. OCLC 907771045.
2. ↑ Kriegeskorte, N., & Kievit, R. A. (2013). Representational geometry: Integrating cognition, computation, and the brain. Trends in Cognitive Sciences, 17(8), 401–412. http://doi.org/10.1016/j.tics.2013.06.007
3. ↑ Gärdenfors, Peter (2000). Conceptual spaces: the geometry of thought. Cambridge, Massachusetts: MIT Press. ISBN 0262071991. OCLC 42389577. https://archive.org/details/conceptualspaces0000gard.
4. ↑ Gärdenfors, Peter (2014). Geometry of meaning: semantics based on conceptual spaces. Cambridge, Massachusetts: MIT Press. ISBN 9780262026789. OCLC 854541601.
5. ↑ Foo, N. (2001). Conceptual Spaces—The Geometry of Thought. AI Magazine, 22(1), 139–140. Retrieved from [1]
6. ↑ Chella, A., & Frixione, M., & Gaglio, S.; (1997). A Cognitive Architecture for Artificial Vision. Artificial Intelligence, 89(1), 73–111. http://doi.org/10.1016/S0004-3702(96)00039-2

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