## Section: New Results

### Modular Systems for Modal Logics

Participant : Lutz Straßburger.

There are modal logics like S4 or K, for which it is rather straightforward to provide a cut-free sequent system, and there are others, like S5 for which this is difficult or impossible. We (in a joint work with Kai Brünnler, Univ. Bern) used “nested sequents” [30] (a generalization of hypersequents [24] ) to give a completely modular account to the whole modal cube below S5. That is to say, we have cut-free sequent systems for the basic normal modal logics formed by any combination of the axioms d, t, b, 4, 5, such that each axiom has a corresponding rule and each combination of these rules is complete for the corresponding frame conditions. This result are published in [16] .