Proof Theory of Modal Logic

This research aims to extend and unify concepts in the proof theory of modal logic and potentially other disciplines.

That means, on the one hand, finding different calculi for modal logic, especially beyond the classical normal classes, i.e. non-normal and intuitionistic logic.

Furthermore, the research might add onto proof systems that include more complex modal logics, like fixpoints and multi-modalities.

On the other hand, I want to investigate the relationships between the different approaches of designing a calculus, especially the structural and the semantically influenced approach. Other potential extensions include circular systems in general. A unification approach that seems very promising is the usage and extension of focussing.