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
see Paper P9.
Aristotelian relations in arbitrary Boolean algebras
see Paper P14.
opposition and implication relations
see Paper P9, Paper P14.
duality relations and their generalizations
see Paper P18, Paper P14.
Aristotelian versus duality relations
see Paper P5, Paper P18.
context-dependence of Aristotelian relations
see Paper P12, Paper P20.
logical complementarities between Aristotelian diagrams
see Paper P7, Paper P10, Paper P11.
Boolean subfamilies of Aristotelian diagrams
see Paper P20.
Boolean closure of Aristotelian diagrams
see Paper P2, Paper P20.
negation asymmetry and lexicalisation
see Book B1

visual-geometric topics

relation between Aristotelian and Hasse diagrams
see Paper P1, Paper P6, Paper P14.
2D versus 3D diagrams
see Paper P1, Paper P11, Paper P13, Talk T15.
subdiagrams embedded inside larger diagrams
see Paper P2, Paper P3, Paper P7, Paper P10, Paper P11, Book B1.
geometrical complementarities between Aristotelian diagrams
see Paper P7, Paper P10, Paper P11.
informational and computational equivalence of Aristotelian diagrams
see Paper P13, Paper P15, Paper P16, Paper S7
cognitive aspects of Aristotelian diagrams
see Paper P6, Paper P13, Paper P15, Paper S7, Talk T15.
cognitive aspects of duality diagrams
see Paper P3.