A categorical interpretation of C. S. Peirce's propositional logic Alpha
This is an interesting paper, concerning the interaction between propositional logic, geometric topology, and category theory. It is very well summarized in the authors' abstract, which we quote: ``\textit{C. S. Peirce}'s graphical system Alpha for propositional logic is given a geometric representation in term of isotopy classes of planar diagrams, and surgery rules on these diagrams called illative transformations. An algebraic representation theorem is proven, stating that Alpha, as an equational theory, is isomorphic to the theory of Boolean algebras. The geometric and algebraic representations are extended to give multi-sorted analogues of Alpha. An interpretation of Alpha is given in terms of linear logic and the theory of closed categories''.
scientific article; zbMATH DE number 1472405