Sequent calculi and interpolation for non-normal modal and deonticlogics

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, it is given a Maehara-style proof of Craig's interpolation theorem for most of the logics considered

A New Method for Bounding the Complexity of Modal Logics

. We present a new proof-theoretic approach to bounding the complexity of the decision problem for propositional modal logics. We formalize logics in a uniform way as sequent systems and then restrict the structural rules for particular systems. This, combined with an analysis of the accessibility relation of the corresponding Kripke structures, yields decision procedures with bounded space requirements. As examples we give O(n log n) space procedures for the modal logics K and T. 1 Introduction We present a new proof-theoretic approach to bounding the complexity of the decision problem for propositional modal logics. We formalize logics in a uniform way as cut-free labelled sequent systems and then restrict the structural rules for particular systems. This, combined with an analysis of the accessibility relation of the corresponding Kripke structures, yields decision procedures with space requirements that are easily bounded. As examples we give O(n log n) space decision procedures f..

A New Method for Bounding the Complexity of Modal Logics

We present a new proof-theoretic approach to bounding the complexity of the decision problem for propositional modal logics. We formalize logics in a uniform way as sequent systems and then restrict the structural rules for particular systems. This, combined with an analysis of the accessibility relation of the corresponding Kripke structures, yields decision procedures with bounded space requirements. As examples we give O(n log n) space procedures for the modal logics K and T