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Tutorial 1

Order-of-Magnitude Reasoning for Alternatives
Assessment and Consensus Measurement

Nuria Agell
ESADE Business School
Universitat Ramon Llull
Barcelona, Spain

(CANCELLED; alternate plans in progress)

Tutorial 2

Mereology, Geometry, and Shapes

Stefano Borgo
Laboratory for Applied Ontology,
Trento, Italy

Mereology, Geometry, and Shapes

by Stefano Borgo

Tutorial 2

About the Tutorial

The tutorial gives an introduction to the perspective of qualitative space representation based on mereology and highlights how geometrical thinking depends on the primitives one adopts. We begin by introducing the motivations for formal theories based on the notion of parthood and connection (mereotopologies) and then present some extensions developed to talk about spatial features (mereogeometries). Beside a formal introduction of these systems, we show how to compare them and how they can be used. We pay particular attention to systems built out of standard geometrical figures like squares, spheres and regular triangles; and play with these to find ways to build other classical figures. Finally, we explore different ways to "understand" Euclidean points in these systems. Throughout the course, ontological considerations and practical manipulation of figures will lead to discuss how to think about geometry.

The course is self-contained and assumes only basic knowledge of Euclidean geometry. Some knowledge of first-order logic would be helpful. Core topics to be covered are:
  1. qualitative geometry and mereological geometry: what and why
  2. introduction to mereology and mereogeometry as formal systems
  3. playing and thinking with geometrical figures
  4. constructing points in mereogeometry
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