A Complete Axiomatisation of Partial Differentiation
Azimuth 2020-05-18
In the eighth talk of the ACT@UCR seminar, Gordon Plotkin will tell us about partial differentiation, viewed as a logical theory.
He will give his talk on Wednesday May 20th at 5 pm UTC, which is 10 am in California, or 1 pm on the east coast of the United States, or 6 pm in England. It will be held online via Zoom, here:
https://ucr.zoom.us/j/607160601
Afterwards we will discuss his talk at the Category Theory Community Server. You can see those discussions here if you become a member:
• Gordon Plotkin, A complete axiomatisation of partial differentiation.
Abstract. 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.