Lattices of modal logics and their groups of automorphisms

✍ Scribed by Marcus Kracht

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 330 KB
• Volume: 100
• Category: Article
• ISSN: 0168-0072
• DOI: 10.1016/s0168-0072(99)00007-x

✦ Synopsis

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 ÿxes all logics of ÿnite codimension. We also obtain the following characterization of pretabular logics containing S4: a logic properly extends a pretabular logic of NExt S4 i its lattice of extensions is ÿnite and linear.