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Expressivity in polygonal, plane mereotopology

Published online by Cambridge University Press:  12 March 2014

Ian Pratt  and
Dominik Schoop
Ian Pratt
Affiliation:
Department of Computer Science, University of Manchester, Oxford Road, Manchester, UK, E-mail: ipratt@cs.man.ac.uk
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Abstract

In recent years, there has been renewed interest in the development of formal languages for describing mereological (part-whole) and topological relationships between objects in space. Typically, the non-logical primitives of these languages are properties and relations such as ‘x is connected’ or ‘x is a part of y’, and the entities over which their variables range are, accordingly, not points, but regions: spatial entities other than regions are admitted, if at all, only as logical constructs of regions. This paper considers two first-order mereotopological languages, and investigates their expressive power. It turns out that these languages, notwithstanding the simplicity of their primitives, are surprisingly expressive. In particular, it is shown that infinitary versions of these languages are adequate to express (in a sense made precise below) all topological relations over the domain of polygons in the closed plane.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 2 , June 2000 , pp. 822 - 838
Copyright
Copyright © Association for Symbolic Logic 2000

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