{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/28313"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/28313","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Mapping spatial relations","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Kasturirangan, Rajesh, 1971-"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Dept. of Brain and Cognitive Sciences.","school":null,"contributors":[],"advisors":["Whitman Richards."],"committee_chairs":[],"committee_members":[],"year":2004,"date_issued":"2004","date_published":"2004","updated_at":"2026-07-22T22:21:43Z","subjects":["Brain and Cognitive Sciences."],"languages":["en_US"],"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. 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