Spheres, Cubes and Simplexes in Mereogeometry

• Authors: Stefano Borgo
• Languages of publication: EN

Abstracts

EN

In 1929 Tarski showed how to construct points in a region-based first-order logic for space representation. The resulting system, called the geometry of solids, is a cornerstone for region-based geometry and for the comparison of point-based and region-based geometries. We expand this study of the construction of points in region-based systems using different primitives, namely hyper-cubes and regular simplexes, and show that these primitives lead to equivalent systems in dimension n ≥ 2. The result is achieved by adopting a single set of definitions that works for both these classes of figures. The analysis of our logics shows that Tarski’s choice to take sphere as the geometrical primitive might be intuitively justified but is not optimal from a technical viewpoint.

Keywords

EN

mereogeometry; geometry of solids; hyper-cube; regular simplex; sphere; mereology

• Publisher: Uniwersytet Mikołaja Kopernika (Nicolaus Copernicus University in Toruń)
• Journal: Logic and Logical Philosophy
• Year: 2013
• Volume: 22
• Issue: 3
• Pages: 255-293

Dates

published

2013-09-01

online

2013-07-02

Contributors

author

Stefano Borgo

• LOA, ISTC CNR Trento and KRDB FUB Bolzano (IT)

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Identifiers

DOI

10.12775/LLP.2013.013