The aim of the paper is to work towards a generalisation of coalgebraic logic enriched over a commutative quantale. Previous work has shown how to dualise the coalgebra type functor $T:\varOmega \text {-}\mathsf {Cat}\rightarrow \varOmega \text {-}\mathsf {Cat}$ in order to obtain the modal operators and axioms describing transitions of type T. Here we give a logical description of the dual of $\varOmega \text {-}\mathsf {Cat}$.