ACT@UCR Seminar: A Complete Axiomatisation of Partial Differentiation - Gordon Plotkin

We formalise the well-known rules of partial differentiation in a version of equational logic with function variables and binding constructs. We prove the resulting theory is complete with respect to polynomial interpretations. The proof makes use of Severi’s theorem that all multivariate Hermite problems are solvable. We also hope to present a number of related results, such as decidability and Hilbert–Post completeness.