Lattices of Modal Logics [PhD Thesis]
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In this thesis we investigate modal logics from a lattice theoretic point of view. There are essentially two well-known methods of research on lattices of modal logics. The investigation of the lattice of modal logics as a whole, and the local investigation of the lattice of extensions of some strong logic. In this thesis we will provide a third one by investigating proper complete sublattices, which are not filters within the whole lattice, but compactness preserving. The framework of our investigation is the lattice of normal n-modal logics, i.e., normal modal logics with n modal operators.
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