Spheres, cubes and simple

Logic and Logical Philosophy 22 (3):255-293 (2013)
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Abstract

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

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References found in this work

Region-based topology.Peter Roeper - 1997 - Journal of Philosophical Logic 26 (3):251-309.
Tarski's system of geometry.Alfred Tarski & Steven Givant - 1999 - Bulletin of Symbolic Logic 5 (2):175-214.
La géométrie dans le monde sensible.Jean Nicod - 1965 - Revue Philosophique de la France Et de l'Etranger 155 (3):383-383.
Mereotopology without Mereology.Peter Forrest - 2010 - Journal of Philosophical Logic 39 (3):229-254.

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