Hypersequent Calculi for Godel Logics -- a Survey

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 Gdel logics. We first describe analytic calculi for propositional finite and infinite-valued Gdel 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 Gdel logic, is also considered.