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The Interaction Between Logic and Geometry in Aristotelian Diagrams

  • Lorenz Demey
  • Hans Smessaert
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9781)

Abstract

We develop a systematic approach for dealing with informationally equivalent Aristotelian diagrams, based on the interaction between the logical properties of the visualized information and the geometrical properties of the concrete polygon/polyhedron. To illustrate the account’s fruitfulness, we apply it to all Aristotelian families of 4-formula fragments that are closed under negation (comparing square and rectangle) and to all Aristotelian families of 6-formula fragments that are closed under negation (comparing hexagon and octahedron).

Keywords

Aristotelian diagram Logical geometry Square of oppositions Hexagon Octahedron Cross-polytope Symmetry group 

Notes

Acknowledgements

We would like to thank Dany Jaspers and Margaux Smets for their valuable feedback on an earlier version of this paper. The first author holds a Postdoctoral Fellowship of the Research Foundation–Flanders (FWO).

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Center for Logic and Analytic PhilosophyKU LeuvenLeuvenBelgium
  2. 2.Department of LinguisticsKU LeuvenLeuvenBelgium

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