logical geometry

logical, linguistic and conceptual systems

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.

Throughout history a variety of authors have constructed logical diagrams for analysing logical, linguistic and conceptual systems such as syllogistics, propositional logic, modal logic, generalized quantifiers, aspectual adverbs, colour concepts and metalogical concepts.

In our own work we have focussed on constructing logical diagrams for:


  • subject negation in syllogistics
  • singular propositions in syllogistics
  • modal logic
  • public announcement logic


  • definite descriptions
  • generalized quantifiers
  • subjective quantifiers
  • proportional quantifiers
  • gradable adjectives

conceptual systems

  • the Aristotelian relations themselves
  • the duality relations themselves
  • abstract ordering relations
  • the metalogical concepts of tautology, satisfiability etc.
  • the logical concepts of dependence and independence