11 January 2022, The Utrecht Logic in Progress Series (TULIPS), Iris van der Giessen

In this TULiPS talk, I will provide a high-level overview of the work of my PhD under supervision of Rosalie Iemhoff and Nick Bezhanishvili. I am studying two topics in the field of proof theory: uniform interpolation and admissible rules. I apply both topics to (intuitionistic) modal logics.

The first is used to describe the form of proof systems in terms of so-called negative results: if a logic does not have uniform interpolation then it cannot have a sequent calculus with certain nice properties. The aim of my research is to widen the scope to proof formalisms such as nested sequents. The second part is a study on the structure of logics. The admissible rules are those rules that you can add to a logic without changing its set of theorems. One of my main results is a characterization of the admissible rules of six interesting intuitionistic modal logics.

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