Automorphisms of the Lattice of Classical Modal Logics

Abstract

In this paper we analyze the propositional extensions of the minimal classical modal logic system E, which form a lattice denoted as CExtE. Our method of analysis uses algebraic calculations with canonical forms, which are a generalization of the normal forms applicable to normal modal logics. As an application, we identify a group of automorphisms of CExtE that is isomorphic to the symmetric group S4.

28 pages, 1 figure