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M. Baaz, A. Ciabattoni, C. Fermüller:
"Hypersequent Calculi for Gödel Logics - a Survey";
Journal of Logic and Computation, 13 (2003), 6; S. 835 - 861.

Hypersequent calculi arise by generalizing standard sequent calculi
to refer to whole contexts of sequents instead of single sequents.
We present a number of results using hypersequents to obtain
a Gentzen-style characterization for the family of Gödel logics.
We first describe analytic calculi for propositional finite and infinite-valued
Gödel logics. We then show that the framework of hypersequents allows one to move straightforwardly
from the propositional level to first-order as well as propositional
quantification. A certain type of modalities, enhancing the expressive power of
Gödel logic, is also considered.