creators_name: Stell, J. G.
creators_name: Worboys, M. F.
editors_name: Hirtle, S. C.
editors_name: Frank, A. U.
type: confpaper
datestamp: 1998-09-24
lastmod: 2011-03-11 08:54:01
metadata_visibility: show
title: The Algebraic Structure of Sets of Regions
ispublished: pub
subjects: comp-sci-art-intel
full_text_status: public
keywords: qualitative spatial reasoning, spatial ontology, vagueness, uncertainty, region-connection calculus, boundaries, spatial mereology, Heyting algebra, bi-Heyting algebra, co-Heyting algebra, GIS, geographic information systems, pointless topology, approximate reasoning, modal operators
abstract: The provision of ontologies for spatial entities is an important topic in spatial information theory. Heyting algebras, co-Heyting algebras, and bi-Heyting algebras are structures having considerable potential for the theoretical basis of these ontologies. This paper gives an introduction to these Heyting structures, and provides evidence of their importance as algebraic theories of sets of regions. The main evidence is a proof that elements of certain Heyting algebras provide models of the Region-Connection Calculus developed by Cohn et al. By using the mathematically well known techniques of ``pointless topology'', it is straightforward to conduct this proof without any need to assume that regions consist of sets of points. Further evidence is provided by a new qualitative theory of regions with indeterminate boundaries. This theory uses modal operators which are related to the algebraic operations present in a bi-Heyting algebra.
date: 1997
date_type: published
publisher: Lecture Notes in Computer Science, volume 1329, Springer Verlag, Berlin
pagerange: 163-174
refereed: FALSE
citation:   Stell, J. G. and Worboys, M. F.  (1997) The Algebraic Structure of Sets of Regions.  [Conference Paper]     
document_url: http://cogprints.org/517/2/cosit-97.ps