Modal interpolation via nested sequents

TitleModal interpolation via nested sequents
Publication TypeJournal Article
Year of Publication2015
AuthorsFitting, M, Kuznets, R
JournalAnnals of pure and applied logic
Date PublishedMarch
AbstractThe main method of proving the Craig Interpolation Property (CIP) constructively uses cut-free sequent proof systems. Until now, however, no such method has been known for proving the CIP using more general sequent-like proof formalisms, such as hypersequents, nested sequents, and labelled sequents. In this paper, we start closing this gap by presenting an algorithm for proving the CIP for modal logics by induction on a nested-sequent derivation. This algorithm is applied to all the logics of the so-called modal cube.