Hypersequents as a uniform framework for Urquhart's C, MTL and related logics

We summarize various results in proof theory of many-valued and related logics that jointly clarify the relations between important logics like MTL, (different versions of) Urquhart's C, contraction-free versions of intuitionistic logic, and Godel logic. The central tool of investigation is the embedding of suitable sequent calculi into hypersequent calculi that include Avron's communication rule.