logical geometry

logical diagrams

The central aim of Logical Geometry is to develop an interdisciplinary framework for the study of logical diagrams in the analysis of logical, linguistic and conceptual systems.

Several authors have studied logical and geometrical properties of various types of logical diagrams, such as the difference between Aristotelian and Duality relations, the notion of Boolean closure and the relation between Aristotelian and Hasse diagrams.

In our own work we have focussed on the following:

abstract-logical topics

  • information contents of the Aristotelian relations
  • Aristotelian relations in arbitrary Boolean algebras
  • opposition and implication relations
  • duality relations and their generalizations
  • Aristotelian versus duality relations
  • context-dependence of Aristotelian relations
  • logical complementarities between Aristotelian diagrams
  • Boolean subfamilies of Aristotelian diagrams
  • Boolean closure of Aristotelian diagrams
  • negation asymmetry and lexicalisation

visual-geometric topics

  • relation between Aristotelian and Hasse diagrams
  • 2D versus 3D diagrams
  • subdiagrams embedded inside larger diagrams
  • geometrical complementarities between Aristotelian diagrams
  • informational and computational equivalence of Aristotelian diagrams
  • cognitive aspects of Aristotelian diagrams
  • cognitive aspects of duality diagrams