Charles Sanders Peirce (1839-1914), a philosopher, logician and scientist, was one of the founders of modern symbolic logic. In particular, he developed a form of predicate logic. Peirce devised a graphical notation, known as existential graphs, to represent logical calculi. There were three systems of such graphs: the system alpha, to represent propositional logic, the system beta, to represent predicate logic, and the system gamma, to represent modal logic.
Geraldine Brady and Todd Trimble have given a category theoretic interpretation of the alpha and beta systems. The latter, a form of string diagrammatic notation, was developed (PontoShul) into a string diagram notation for indexed monoidal categories.
Geraldine Brady and Todd Trimble (2000a). A Categorical Interpretation of C. S. Peirce’s Propositional Logic Alpha. Journal of Pure and Applied Algebra 149 (2000): 213-239
Geraldine Brady and Todd Trimble (2000b). A String Diagram Calculus for Predicate Logic and C. S. Peirce's System Beta, preprint
Kate Ponto and Mike Shulman, Duality and traces in indexed monoidal categories, (web)