Sequent Calculi and Interpolation for Non-Normal Modal and Deontic Logics

Eugenio Orlandelli
2020 Logic and Logical Philosophy  
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,
more » ... 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.
doi:10.12775/llp.2020.018 fatcat:qi3ijgiwwjag3murwosx3eotiq