Tomorrow (Monday 22 November 2021, at 9:40 Central European Time) I will give a talk on “Deductive systems and Grothendieck topologies” for the Dagstuhl Seminar Geometric Logic, Constructivisation, and Automated Theorem Proving.

The abstract is as follows:

I will show that the classical proof system of geometric logic over a given geometric theory is equivalent to new proof systems based on the notion of Grothendieck topology. These equivalences result from a proof-theoretic interpretation of the duality between the quotients of a given geometric theory and the subtoposes of its classifying topos. Interestingly, these alternative proof systems turn out to be computationally better-behaved than the classical one for many purposes, as I will illustrate by discussing a few selected applications.

To attend the talk, you may click here.