Hypersequent
(Proof Theory)
Tech
What is Hypersequent?
In mathematical logic, the hypersequent framework is an extension of the proof-theoretical framework of sequent calculi used in structural proof theory to provide analytic calculi for logics which are not captured in the sequent framework. A hypersequent is usually taken to be a finite multiset of ordinary sequents, written The sequents making up a hypersequent are called components. The added expressivity of the hypersequent framework is provided by rules manipulating different components, such as the communication rule for intermediate logic LC (below left) or the modal splitting rule for modal logic S5 (below right): Hypersequent calculi have been used to treat modal logics, intermediate logics, and substructural logics. Hypersequents usually have a formula interpretation, i.e., are interpreted by a formula in the object language, nearly always as some kind of disjunction. The precise formula interpretation depends on the considered logic.