We introduce labelled sequent calculi for the basic normal non-distri-butive modal logic and
31 of its axiomatic extensions, where the labels are atomic formulas of a first order language
which is interpreted on the canonical extensions of the algebras in the variety corresponding
to the logic. Modular proofs are presented that these calculi are all sound, complete and
conservative wrt, and enjoy cut elimination and the subformula property. The introduction of
these calculi showcases a general methodology for introducing labelled calculi for the class …

We introduce labelled sequent calculi for the basic normal non-distributive modal logic L
and 31 of its axiomatic extensions, where the labels are atomic formulas of a first order
language which is interpreted on the canonical extensions of the algebras in the variety
corresponding to the logic L. Modular proofs are presented that these calculi are all sound,
complete and conservative wrt L, and enjoy cut elimination and the subformula property. The
introduction of these calculi showcases a general methodology for introducing labelled …