Ontologies for plane, polygonal mereotopology
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.
logical systems for reasoning about polyhedra
scientific article; zbMATH DE number 1129582
scientific article