Lattices of modal logics and their groups of automorphisms

The present paper investigates the groups of automorphisms for some lattice s of modal logics. The main results are the following. The lattice of norma l extensions of S4.3, NExtS4.3, has exactly two automorphisms, NExt K.alt(1 ) has continuously many automorphisms. Moreover, any automorphism of NExtS4 fixes all logics of finite codimension; We also obtain the following chara cterization of pretabular logics containing S4: a logic properly extends a pretabular logic of NExtS4 iff its lattice of extensions is finite and line ar. (C) 1999 Elsevier Science B.V. All rights reserved.