Modal interpolation via nested sequents

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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.

MSC

03B45
03C40
03F07
03B70

Keywords

Craig interpolation
Nested sequent
Structural proof theory
Modal logic

Cited by (0)

1

This collaboration was made possible by several visits of this author to Bern, thanks to the financial support of the Swiss National Science Foundation Grants 200020-134740 and PZ00P2-131706.

2

In 2011–2013, this author was supported by the Swiss National Science Foundation Grant PZ00P2-131706. The final stages of the research were supported by the Austrian Science Fund Grants Y 544 and P 25417.

3

Affiliation b of this author corresponds to the period up until February 2014, when most of the work on this paper was done. Affiliation c of this author is his current affiliation and corresponds to the preparation of the final version of the paper.