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[2602.23302] The logic of KM belief update is contained in the logic of AGM belief revision
Summary
This paper explores the relationship between KM belief update and AGM belief revision, demonstrating that AGM can be viewed as a specific instance of KM. It establishes modal logic connections between the two frameworks, highlighting key axioms and their implications.
Why It Matters
Understanding the interplay between KM belief updates and AGM belief revisions is crucial for advancements in artificial intelligence and logic. This paper provides foundational insights that could enhance decision-making processes in AI systems, impacting areas such as knowledge representation and reasoning.
Key Takeaways
- AGM belief revision can be seen as a special case of KM belief update.
- The paper establishes a modal logic framework linking KM and AGM axioms.
- Every axiom of KM is a theorem in AGM, indicating a hierarchical relationship.
- The distinction between KM and AGM can be narrowed to a single axiom regarding unsurprising information.
- These insights may influence future research in AI and logic.
Computer Science > Artificial Intelligence arXiv:2602.23302 (cs) [Submitted on 26 Feb 2026] Title:The logic of KM belief update is contained in the logic of AGM belief revision Authors:Giacomo Bonanno View a PDF of the paper titled The logic of KM belief update is contained in the logic of AGM belief revision, by Giacomo Bonanno View PDF HTML (experimental) Abstract:For each axiom of KM belief update we provide a corresponding axiom in a modal logic containing three modal operators: a unimodal belief operator $B$, a bimodal conditional operator $>$ and the unimodal necessity operator $\square$. We then compare the resulting logic to the similar logic obtained from converting the AGM axioms of belief revision into modal axioms and show that the latter contains the former. Denoting the latter by $\mathcal L_{AGM}$ and the former by $\mathcal L_{KM}$ we show that every axiom of $\mathcal L_{KM}$ is a theorem of $\mathcal L_{AGM}$. Thus AGM belief revision can be seen as a special case of KM belief update. For the strong version of KM belief update we show that the difference between $\mathcal L_{KM}$ and $\mathcal L_{AGM}$ can be narrowed down to a single axiom, which deals exclusively with unsurprising information, that is, with formulas that were not initially disbelieved. Comments: Subjects: Artificial Intelligence (cs.AI); Logic in Computer Science (cs.LO); Logic (math.LO) Cite as: arXiv:2602.23302 [cs.AI] (or arXiv:2602.23302v1 [cs.AI] for this version) https://doi.o...