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:

logic

subject negation in syllogistics
see Paper P12.
singdlar propositions in syllogistics
see Paper P2.
modal logic
see Paper P1.
public announcement logic
see Paper P4, Paper P20.

linguistics

definite descriptions
see Paper S3.
generalized quantifiers
see Paper P1.
subjective quantifiers
see Paper P11, Talk T19.
proportional quantifiers
see Talk T24.
gradable adjectives
see Book B1.

conceptual systems

the Aristotelian relations themselves
see Paper P8, Paper P14.
the duality relations themselves
see Paper P14.
abstract ordering relations
see Paper P14, Talk L7.
the metalogical concepts of tautology, satisfiability etc.
see Paper S2, Paper P14.
the logical concepts of dependence and independence
in preparation.