Fitting, M., & Kuznets, R. (2015). Modal Interpolation via Nested Sequents. Annals of Pure and Applied Logic, 166(3), 274–305. https://doi.org/10.1016/j.apal.2014.11.002
Logic; Craig interpolation; modal logic; nested sequent; structural proof theory
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Abstract:
The 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.
