Automorphisms of the Lattice of Classical Modal Logics

TL;DR

This paper investigates the structure of propositional extensions of the minimal classical modal logic E, revealing a group of automorphisms isomorphic to S4 through algebraic analysis of canonical forms.

Contribution

It introduces a novel algebraic method using canonical forms to analyze the automorphisms of the lattice of classical modal logics.

Findings

Identifies a group of automorphisms isomorphic to S4

Develops algebraic calculations with canonical forms for modal logic

Provides insights into the symmetry structure of propositional modal extensions

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.