11 research outputs found
Cut-elimination for the modal Grzegorczyk logic via non-well-founded proofs
We present a sequent calculus for the modal Grzegorczyk logic Grz allowing
non-well-founded proofs and obtain the cut-elimination theorem for it by
constructing a continuous cut-elimination mapping acting on these proofs.Comment: WOLLIC'17, 12 pages, 1 appendi
Proving Craig and Lyndon Interpolation Using Labelled Sequent Calculi
We have recently presented a general method of proving the fundamental
logical properties of Craig and Lyndon Interpolation (IPs) by induction on
derivations in a wide class of internal sequent calculi, including sequents,
hypersequents, and nested sequents. Here we adapt the method to a more general
external formalism of labelled sequents and provide sufficient criteria on the
Kripke-frame characterization of a logic that guarantee the IPs. In particular,
we show that classes of frames definable by quantifier-free Horn formulas
correspond to logics with the IPs. These criteria capture the modal cube and
the infinite family of transitive Geach logics