2026-09-18T22:15:10Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/283132022-01-13T07:54:17Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Whitman Richards.
Kasturirangan, Rajesh, 1971-
Massachusetts Institute of Technology. Dept. of Brain and Cognitive Sciences.
Massachusetts Institute of Technology. Department of Brain and Cognitive Sciences
2005-09-26T19:43:28Z
2005-09-26T19:43:28Z
2004
2004
http://hdl.handle.net/1721.1/28313
55636098
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Brain and Cognitive Sciences, 2004.
Includes bibliographical references (p. 155-160).
One of the fundamental issues in cognitive science is the problem of grounding concepts in the perceptual world. In this thesis, I present a computational theory for how spatial relations are grounded in the perceptual world. Three constraints are critical to this theory: abstractness, groundedness and flexibility all of which need to be satisfied in order to explain the structure of spatial concepts. I then show how a formal framework, based on the mathematical notions of category theory can be used to model the grounding problem. The key computational ideas are that of minimal mapping and derivations. A minimal mapping of two categories, A and B, is the "smallest' category, C, that contains A and B. A derivation is a sequence of categories that follow a minimal mapping rule. Derivations and minimal mappings are used to model three domains - the semantics of prepositions, the structure of a toy "Jigsaw World" and the semantics of generic terms and quantifiers. In each case, I show how the computational theory gives rise to insights that are not available upon a purely empirical analysis. In particular, the derivational account shows the importance of stable, non-accidental features and of multiple scales in spatial cognition.
by Rajesh Kasturirangan.
Ph.D.
160 p.
7782113 bytes
7804192 bytes
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Massachusetts Institute of Technology
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http://dspace.mit.edu/handle/1721.1/7582
Brain and Cognitive Sciences.
Mapping spatial relations
Thesis
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Publication
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