  We introduce proper display calculi for basic monotonic modal logic, the
conditional logic CK and a number of their axiomatic extensions. These calculi
are sound, complete, conservative and enjoy cut elimination and subformula
property. Our proposal applies the multi-type methodology in the design of
proper display calculi, starting from a semantic analysis which motivates
syntactic translations from single-type non-normal modal logics to multi-type
normal poly-modal logics.
