Please expand.
Hypersequents appear to have been introduced by Mints in 1968 in order to prove cut elimination for the modal logic S5.
Avron, Arnon. 1996. ‘The Method of Hypersequents in the Proof Theory of Propositional Non-Classical Logics’. In Logic: From Foundations to Applications, edited by Wilfrid Hodges, Martin Hyland, Charles Steinhorn, and John Truss, 1–32. Clarendon Press. [pdf]
@incollection{avron_1996,
title = {The method of hypersequents in the proof theory of propositional non-classical logics},
booktitle = {Logic: from {Foundations} to {Applications}},
publisher = {Clarendon Press},
author = {Avron, Arnon},
editor = {Hodges, Wilfrid and Hyland, Martin and Steinhorn, Charles and Truss, John},
year = {1996},
pages = {1--32}
}