On the complemented disk algebra

Li, S; Li, Y

On the complemented disk algebra

Li, S

Li, Y

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Publication Type:: Journal Article
Citation:: Journal of Logic and Algebraic Programming, 2006, 66 (2), pp. 195 - 211
Issue Date:: 2006-02-01

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Field	Value	Language
dc.contributor.author	Li, S https://orcid.org/0000-0002-3332-2546	en_US
dc.contributor.author	Li, Y	en_US
dc.date.issued	2006-02-01	en_US
dc.identifier.citation	Journal of Logic and Algebraic Programming, 2006, 66 (2), pp. 195 - 211	en_US
dc.identifier.issn	1567-8326	en_US
dc.identifier.uri	http://hdl.handle.net/10453/8254
dc.description.abstract	The importance of relational methods in temporal and spatial reasoning has been widely recognised in the last two decades. A quite large part of contemporary spatial reasoning is concerned with the research of relation algebras generated by the "part of" and "connection" relations in various domains. This paper is devoted to the study of one particular relation algebra appeared in the literature, viz. the complemented disk algebra. This algebra was first described by Düntsch [I. Düntsch, A tutorial on relation algebras and their application in spatial reasoning, Given at COSIT, August 1999, Available from: 〈http://www.cosc.brocku.ca/ ~duentsch/papers/relspat.html〉] and then, Li et al. [Y. Li, S. Li, M. Ying, Relational reasoning in the Region Connection Calculus, Preprint, 2003, Available from: http://arxiv.org/abs/cs/0505041] showed that closed disks and their complements provides a representation. This set of regions is rather restrictive and, thus, of limited practical values. This paper will provide a general method for generating representations of this algebra in the framework of Region Connection Calculus. In particular, connected regions bounded by Jordan curves and their complements is also such a representation. © 2005 Elsevier Inc. All rights reserved.	en_US
dc.relation.ispartof	Journal of Logic and Algebraic Programming	en_US
dc.relation.isbasedon	10.1016/j.jlap.2005.04.003	en_US
dc.subject.classification	Computation Theory & Mathematics	en_US
dc.title	On the complemented disk algebra	en_US
dc.type	Journal Article
utslib.citation.volume	2	en_US
utslib.citation.volume	66	en_US
utslib.for	0102 Applied Mathematics	en_US
utslib.for	01 Mathematical Sciences	en_US
utslib.for	08 Information and Computing Sciences	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	2	en_US
pubs.publication-status	Published	en_US
pubs.volume	66	en_US

Abstract:

The importance of relational methods in temporal and spatial reasoning has been widely recognised in the last two decades. A quite large part of contemporary spatial reasoning is concerned with the research of relation algebras generated by the "part of" and "connection" relations in various domains. This paper is devoted to the study of one particular relation algebra appeared in the literature, viz. the complemented disk algebra. This algebra was first described by Düntsch [I. Düntsch, A tutorial on relation algebras and their application in spatial reasoning, Given at COSIT, August 1999, Available from: 〈http://www.cosc.brocku.ca/ ~duentsch/papers/relspat.html〉] and then, Li et al. [Y. Li, S. Li, M. Ying, Relational reasoning in the Region Connection Calculus, Preprint, 2003, Available from: http://arxiv.org/abs/cs/0505041] showed that closed disks and their complements provides a representation. This set of regions is rather restrictive and, thus, of limited practical values. This paper will provide a general method for generating representations of this algebra in the framework of Region Connection Calculus. In particular, connected regions bounded by Jordan curves and their complements is also such a representation. © 2005 Elsevier Inc. All rights reserved.

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http://hdl.handle.net/10453/8254