A modal logic translation of the AGM axioms for belief revision

TL;DR

This paper introduces a modal logic framework with three operators that precisely captures the AGM axioms for belief revision, linking modal properties to belief change principles.

Contribution

It provides a novel modal logic translation of AGM belief revision axioms, connecting them to Kripke frame properties for formal analysis.

Findings

Modal axioms correspond to AGM axioms

Kripke frame properties characterize belief revision

Framework unifies modal logic and belief change theory

Abstract

Building on the analysis of Bonanno (Artificial Intelligence, 2025) we introduce a simple modal logic containing three modal operators: a unimodal belief operator, a bimodal conditional operator and the unimodal global operator. For each AGM axiom for belief revision, we provide a corresponding modal axiom. The correspondence is as follows: each AGM axiom is characterized by a property of the Kripke-Lewis frames considered in Bonanno (Artificial Intelligence, 2025) and, in turn, that property characterizes the proposed modal axiom.