Ontologies for plane, polygonal mereotopology
type: Item
instance of: scholarly article
title: Ontologies for plane, polygonal mereotopology
zbMATH Open document ID: 0897.03014
author: Ian Pratt
author: Oliver Lemon
published in: Notre Dame Journal of Formal Logic
publication date: 1998-10-19T00:00:00Z
review text: The authors give models for logical systems for reasoning about polyhedra defined in a rather abstract way since the point of the authors' efforts is the demonstration of a logical framework that may be used for certain geometric reasonings while avoiding any reference to points. (Speaking of elementary geometry, one might take exception with the authors' statement that analytic geometry presents a model for geometric reasoning based on the only primitive notion of ``point''. In fact, analytic geometry gives only a framework for constructing models, since one must use another undefined primitive, ``line'', that might be modelled either by \(ax+ by+ c=0\), by \((x- a)^2+ y^2- r^2= 0\), or by some other set of equations.) The main result shows that a model based on polygons given by rational coordinates is, in a restricted sense, a minimal model for reasoning in the Boolean algebra generated from polygons by the operations of join and intersection.
Mathematics Subject Classification ID: 03B30
Mathematics Subject Classification ID: 51M99
Mathematics Subject Classification ID: 03C99
zbMATH DE Number: 1129582
zbMATH Keywords: logical systems for reasoning about polyhedra
zbMATH Keywords: elementary geometry
zbMATH Keywords: geometric reasoning
zbMATH Keywords: polygons
zbMATH Keywords: minimal model
zbMATH Keywords: Boolean algebra
reviewed by: Heinrich Guggenheimer
Wikidata QID: Q114598326
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1305/ndjfl/1039724888
OpenAlex ID: W2114803430
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DOI: 10.1305/NDJFL/1039724888
description: scientific article; zbMATH DE number 1129582