Cf: Category Theory • Jon Awbrey

I opened a topic in the “logic” stream of “category theory.zulipchat” to discuss differential logic in a category theoretic environment and began by linking a few basic resources.

The topic on logical graphs introduced a style of graph-theoretic syntax for propositional logic stemming from the work of Charles S. Peirce and G. Spencer Brown and touched on a generalization of Peirce’s and Spencer Brown’s tree-like forms to what graph theorists know as cactus graphs or cacti.

Somewhat serendipitously, as it turns out, this cactus syntax is just the thing we need to develop differential propositional calculus, which augments ordinary propositional calculus in the same way the differential calculus of Leibniz and Newton augments the analytic geometry of Descartes.

Resources

• Differential Logic • Overview
• Survey of Differential Logic

cc: Category Theory • Cybernetics • Ontolog • Structural Modeling • Systems Science
cc: FB | Differential Logic • Laws of Form