Expressivity in polygonal, plane mereotopology

Journal of Symbolic Logic 65 (2):822-838 (2000)
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
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DOI 10.2307/2586573
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References found in this work BETA
Region-Based Topology.Peter Roeper - 1997 - Journal of Philosophical Logic 26 (3):251-309.
A Calculus of Individuals Based on ``Connection''.Bowman L. Clarke - 1981 - Notre Dame Journal of Formal Logic 22 (3):204-218.
Topological Reasoning and the Logic of Knowledge.Andrew Dabrowski, Lawrence S. Moss & Rohit Parikh - 1996 - Annals of Pure and Applied Logic 78 (1-3):73-110.
Individuals and Points.Bowman L. Clark - 1985 - Notre Dame Journal of Formal Logic 26 (1):61-75.

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Citations of this work BETA
A Proof System for Contact Relation Algebras.Ivo Düntsch & Ewa Orłowska - 2000 - Journal of Philosophical Logic 29 (3):241-262.
A Topological Constraint Language with Component Counting.Ian Pratt-Hartmann - 2002 - Journal of Applied Non-Classical Logics 12 (3-4):441-467.
Full Mereogeometries.Stefano Borgo & Claudio Masolo - 2010 - Review of Symbolic Logic 3 (4):521-567.
A Canonical Model of the Region Connection Calculus.Jochen Renz - 2002 - Journal of Applied Non-Classical Logics 12 (3-4):469-494.

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