Talk: Rosalie Iemhoff (Utrecht)

Title:

The existence of proof systems

Abstract:

Proof systems can be useful to investigate logics, but certainly not all of them are. Usually one requires that a proof system satisfies certain properties that guarantee its usefulness. Hence the question emerges: given certain properties, which logics do have a proof system satisfying them and which logics do not?

Questions of this form, for specific logics, proof systems and properties, form the overarching motivation for this talk. Here we focus on intermediate and modal logics, on a class of proof systems called sequent calculi, and a collection of natural properties on sequent calculi that separates the ''good'' sequent calculi from the others.

During the last decades there have appeared many existence results, stating that a certain logic has a good sequent calculus. However, nonexistence results stating that a given logic does not have a good sequent calculus are much more rare, and in the literature there are only few proposals how to address this problem. In this talk we discuss such a proposal.