Mapping spatial relations

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Brain and Cognitive Sciences.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2004

Author dc:creator

• Kasturirangan, Rajesh, 1971-

Advisor dc:contributor.advisor

• Whitman Richards.

• Brain and Cognitive Sciences.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

en_US

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/28313

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/28313