On countable RCC models

Li, S; Ying, M; Li, Y

On countable RCC models

Li, S

Ying, M

Li, Y

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Publication Type:: Journal Article
Citation:: Fundamenta Informaticae, 2005, 65 (4), pp. 329 - 351
Issue Date:: 2005-09-07

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Field	Value	Language
dc.contributor.author	Li, S https://orcid.org/0000-0002-3332-2546	en_US
dc.contributor.author	Ying, M https://orcid.org/0000-0003-4847-702X	en_US
dc.contributor.author	Li, Y	en_US
dc.date.issued	2005-09-07	en_US
dc.identifier.citation	Fundamenta Informaticae, 2005, 65 (4), pp. 329 - 351	en_US
dc.identifier.issn	0169-2968	en_US
dc.identifier.uri	http://hdl.handle.net/10453/8989
dc.description.abstract	Region Connection Calculus (RCC) is the most widely studied formalism of Qualitative Spatial Reasoning. It has been known for some time that each connected regular topological space provides an RCC model. These 'standard' models are inevitable uncountable and regions there cannot be represented finitely. This paper, however, draws researchers' attention to RCC models that can be constructed from finite models hierarchically. Compared with those 'standard' models, these countable models have the nice property that regions where can be constructed in finite steps from basic ones. We first investigate properties of three countable models introduced by Düuntsch, Stell, Li and Ying, resp. In particular, we show that (i) the contact relation algebra of our minimal model is not atomic complete; and (ii) these three models are non-isomorphic. Second, for each n>0, we construct a countable RCC model that is a sub-model of the standard model over the Euclidean unit n-cube; and show that all these countable models are non-isomorphic. Third, we show that every finite model can be isomorphically embedded in any RCC model. This leads to a simple proof for the result that each consistent spatial network has a realization in any RCC model.	en_US
dc.relation.ispartof	Fundamenta Informaticae	en_US
dc.subject.classification	Computation Theory & Mathematics	en_US
dc.title	On countable RCC models	en_US
dc.type	Journal Article
utslib.citation.volume	4	en_US
utslib.citation.volume	65	en_US
utslib.for	0802 Computation Theory and Mathematics	en_US
utslib.for	0801 Artificial Intelligence and Image Processing	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Strength - QSI - Centre for Quantum Software and Information
utslib.copyright.status	closed_access
pubs.issue	4	en_US
pubs.publication-status	Published	en_US
pubs.volume	65	en_US

Abstract:

Region Connection Calculus (RCC) is the most widely studied formalism of Qualitative Spatial Reasoning. It has been known for some time that each connected regular topological space provides an RCC model. These 'standard' models are inevitable uncountable and regions there cannot be represented finitely. This paper, however, draws researchers' attention to RCC models that can be constructed from finite models hierarchically. Compared with those 'standard' models, these countable models have the nice property that regions where can be constructed in finite steps from basic ones. We first investigate properties of three countable models introduced by Düuntsch, Stell, Li and Ying, resp. In particular, we show that (i) the contact relation algebra of our minimal model is not atomic complete; and (ii) these three models are non-isomorphic. Second, for each n>0, we construct a countable RCC model that is a sub-model of the standard model over the Euclidean unit n-cube; and show that all these countable models are non-isomorphic. Third, we show that every finite model can be isomorphically embedded in any RCC model. This leads to a simple proof for the result that each consistent spatial network has a realization in any RCC model.

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http://hdl.handle.net/10453/8989