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. A development also appears in MellZeil.
Peirce’s philosophy can be seen as Schellingism transformed in light of (in Peirce’s time) modern physics, as Peirce himself notes in an 1894 letter to William James:
My views were probably influenced by Schelling - by all stages of Schelling, but especially the Philosophie der Natur. I consider Schelling as enormous, and one thing I admire about him is his freedom from the trammels of system, and his holding himself uncommitted to any previous utterance. in that, he is like a scientific man. If you were to call my philosophy Schellingism transformed in the light of modern physics, I should not take it hard.
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)
Fernando Zalamea (2012), Peirce’s Logic of Continuity: A Conceptual and Mathematical Approach
Frederik Stjernfelt (2014), Natural Propositions: The Actuality of Peirce’s Doctrine of Dicisigns
Rosa Maria Perez-Teran Mayorga (2008), From Realism to ‘Realicism’: The Metaphysics of Charles Sanders Peirce
Andrew Reynolds (2002), Peirce’s Scientific Metaphysics: The Philosophy of Chance, Law, and Evolution
Matthew Moore (ed) (2010), New Essays on Peirce’s Mathematical Philosophy
Louis Kauffman (2001), The Mathematics of Charles Sanders Peirce
C.S. Peirce & Matthew Moore (ed) (2010), Philosophy of Mathematics: Selected Writings
Paul-André Melliès and Noam Zeilberger (2016) A bifibrational reconstruction of Lawvere’s presheaf hyperdoctrine, (arXiv:1601.06098, cs.LO)