 To obtain a hypersequent calculus for the fundamental fuzzy logic MTL one has to add the communication rule to a sequent system for the contraction-free version of intuitionistic logic (a well-studied example of a  substructural logic).  Analytic proof systems for other fuzzy logics, in particular Łukasiewicz logic, call for a more radical departure from traditional calculi, where the sequent components of hypersequents are interpreted differently than intuitionistic or classical sequents. Also labeled proof systems and various tableau calculi have been suggested. A detailed presentation of the corresponding state of the art can be found in Metcalfe, Olivetti, &amp; Gabbay 2008 and Metcalfe 2011.