Proof systems for the coalgebraic cover modality

@inproceedings{Blkov2008ProofSF,
  title={Proof systems for the coalgebraic cover modality},
  author={Marta B{\'i}lkov{\'a} and Alessandra Palmigiano and Yde Venema},
  booktitle={Advances in Modal Logic},
  year={2008}
}
We investigate an alternative presentation of classical and positive modal logic where the coalgebraic cover modality is taken as primitive. For each logic, we present a sound and complete Hilbert-style axiomatization. Moreover, we give a two-sided sound and complete sequent calculus for the negation-free language, and for the language with negation we provide a one-sided sequent calculus which is sound, complete and cut-free. 
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