There’s a nice interplay between geometric and logical dualities in C.S. Peirce’s graphical systems of logic, rooted in his discovery of the amphecks and and flowering in his logical graphs for propositional and predicate calculus. Peirce’s logical graphs bear the dual interpretations he dubbed entitative and existential graphs.
Here’s a Table of Boolean Functions on Two Variables, using an extension of Peirce’s graphs from trees to cacti, illustrating the duality so far as it affects propositional calculus.
- Logic Syllabus
- Logical Graphs
- Cactus Language
- Futures Of Logical Graphs
- Minimal Negation Operators
- Survey of Theme One Program
- Survey of Animated Logical Graphs
- Propositional Equation Reasoning Systems
- Applications • Constraint Satisfaction Problems