Lattices of modal logics and their groups of automorphisms Original Research Article

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, NExtView the MathML source, has exactly two automorphisms, NExtView the MathML source has continuously many automorphisms. Moreover, any automorphism of NExtView the MathML source 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 NExtView the MathML source iff its lattice of extensions is finite and linear.