G3-style sequent calculi for the logics in the cube of non-normal modal logics and for their deontic extensions are studied. For each calculus we prove that weakening and contraction are height-preserving admissible, and we give a syntactic proof of the admissibility of cut. This implies that the subformula property holds and that derivability can be decided by a terminating proof search whose complexity is in Pspace. These calculi are shown to be equivalent to the axiomatic ones and, therefore, they are sound and complete with respect to neighbourhood semantics. Finally, a Maehara-style proof of Craig’s interpolation theorem for most of the logics considered is given.
Keywords non-normal logics  deontic logics  sequent calculi  structural proof theory  interpolation  decidability
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DOI 10.12775/llp.2020.018
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Gentle Murder, or the Adverbial Samaritan.James William Forrester - 1984 - Journal of Philosophy 81 (4):193-197.
On the Semantic Non-Completeness of Certain Lewis Calculi.Sören Halldén - 1951 - Journal of Symbolic Logic 16 (2):127 - 129.

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