Webpage of the Compositional Systems and Methods group at TalTech.

**Nathan Haydon**, Taltech

Compositional Diagrammatic First-Order Logic

Peirce’s Existential Graphs (EGs) arose from his continued study of the logic of relations. I’ll give a brief introduction to Peirce’s Existential Graphs and will then show how the Beta variant is closely related to the algebraic structure found in cartesian bicategories of relations. In the context of string diagrams, lines of identity obey the laws of special Frobenius algebras, while derivations in the negation-free fragment are the 2-cells of free cartesian bicategories. I’ll conclude with a working example of our compositional diagrammatic language — what we call D_Beta — that shares the iconic features of Peirce’s EGs.