Lattices of Modal Logics and Their Groups of Automorphisms

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.alt1 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.

• Type: Journal
• Year: 1999
• Where: APAL
• Authors: Marcus Kracht
• Keywords: APAL 1999, Automorphism, Logic, Pretabular Logic