Deep sequents for modal logic

Dear fellow amphibians,

I finally finished a paper in which I give systems in the calculus of
structures for all the normal modal logics of the "cube" formed from
the axioms d,t,b,4,5. It turned out that the full depth of the
calculus of structures is not needed, so I introduce systems somewhat
intermediate between sequent calculus and calculus of structures.

As usual, the paper is available from www.iam.unibe.ch/~kai/ .
Comments are welcome!

Best wishes,

-Kai