Hypersequent Calculi - Theory and Application

Abstract

The present work is a methodological study on different methods of proving cut eliminability in the framework of hypersequent calculi. In particular we provide axiomatic and semantical characterization of modal logic S5 which will serve as a running example of logic for which several solutions were provided. A problem of cut rule and its elimination will be discussed in general and we will show why this result fails to hold for standard sequent calculus for S5. We will introduce hypersequent calculi and characterize several solutions provided for S5 in this setting. Also we will illustrate different methods of proof of cut elimination in hypersequent calculi such a semantical way of proving a system cut-free and a syntactical proof of cut elimination, a general strategy of proof for hyperseunet calculi. Finally we brifly describe a new approach to hypersequents which is based on their interpretation as finite lists of sequents.