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POINT-FREE GEOMETRY, OVALS, AND HALF-PLANES

Published online by Cambridge University Press:  23 January 2017

GIANGIACOMO GERLA  and
RAFAŁ GRUSZCZYŃSKI
GIANGIACOMO GERLA*
Affiliation:
The International Institute for Advanced Scientific Studies (IIASS)
RAFAŁ GRUSZCZYŃSKI*
Affiliation:
Department of Logic, Nicolaus Copernicus University in Toruń
*
*THE INTERNATIONAL INSTITUTE FOR ADVANCED SCIENTIFIC STUDIES (IIASS) SALERNO, ITALY E-mail: [email protected]URL: www.ggerla.it
†DEPARTMENT OF LOGIC NICOLAUS COPERNICUS UNIVERSITY IN TORUŃ POLAND E-mail: [email protected]URL: www.umk.pl/∼gruszka
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Abstract

In this paper we develop a point-free system of geometry based on the notions of region, parthood, and ovality, the last one being a region-based counterpart of the notion of convex set. In order to show that the system we propose is sufficient to reconstruct an affine geometry we make use of a theory of a Polish mathematician Aleksander Śniatycki from [15], in which the concept of half-plane is assumed as basic.

Keywords

00A3051A3552A01point-free geometryfoundations of geometryaffine geometryconvexityBoolean algebrasmereology
Type
Research Article
Information
The Review of Symbolic Logic , Volume 10 , Issue 2 , June 2017 , pp. 237 - 258
Copyright
Copyright © Association for Symbolic Logic 2017 

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