Abstract
The present paper investigates the groups of automorphisms for some lattices of modal logics. The main results are the following. The lattice of normal extensions of S4.3, NExt S4.3 , has exactly two automorphisms, NExt K.alt 1 has continuously many automorphisms. Moreover, any automorphism of NExt S4 fixes all logics of finite codimension. We also obtain the following characterization of pretabular logics containing S4: a logic properly extends a pretabular logic of NExt S4 iff its lattice of extensions is finite and linear.
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