Proof systems for the coalgebraic cover modality

We investigate an alternative presentation of classical and pos- itive modal logic where the coalgebraic cover modality is taken as primitive. For each logic, we present a sound and complete Hilbert-styl e axiomatiza- tion. Moreover, we give a two-sided sound and complete seque nt calculus for the negation-free language, and for the language with negat ion we provide a one-sided sequent calculus which is sound, complete and cu t-free.

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