The logic of KM belief update is contained in the logic of AGM belief revision
#belief update #belief revision #KM logic #AGM logic #modal logic #artificial intelligence #reasoning systems #Katsuno-Mendelzon
📌 Key Takeaways
- Giacomo Bonanno proved KM belief update logic is contained within AGM belief revision logic
- The research translates both frameworks into modal logic with belief, conditional, and necessity operators
- AGM belief revision can be seen as a special case of KM belief update
- The difference between strong versions of these frameworks reduces to a single axiom about unsurprising information
- This advance provides a more comprehensive framework for understanding belief change in AI systems
📖 Full Retelling
Computer science researcher Giacomo Bonanno published a groundbreaking paper on February 26, 2026, demonstrating that the logic of KM belief update is contained within the logic of AGM belief revision, advancing theoretical understanding of artificial intelligence reasoning systems. The paper, submitted to the arXiv repository, establishes a fundamental relationship between two prominent frameworks for modeling how intelligent systems update their beliefs when encountering new information. By translating axioms from both KM (Katsuno-Mendelzon) belief update and AGM (Alchourrón-Gärdenfors-Makinson) belief revision into modal logic with operators for belief, conditional statements, and necessity, Bonanno reveals that the latter framework encompasses the former. This theoretical breakthrough demonstrates that AGM belief revision can be understood as a special case of KM belief update, providing researchers with a more comprehensive framework for understanding belief change in artificial intelligence systems. The paper further narrows the difference between the strong versions of these frameworks to a single axiom dealing with unsurprising information, offering new insights into how AI systems process information that doesn't contradict their existing beliefs.
🏷️ Themes
Artificial Intelligence, Logic Systems, Belief Revision, Theoretical Computer Science
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Original Source
--> Computer Science > Artificial Intelligence arXiv:2602.23302 [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 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_ $ and the former by $\mathcal L_ $ we show that every axiom of $\mathcal L_ $ is a theorem of $\mathcal L_ $. 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_ $ and $\mathcal L_ $ can be narrowed down to a single axiom, which deals exclusively with unsurprising information, that is, with formulas that were not initially disbelieved. Comments: arXiv admin note: text overlap with arXiv:2310.11506 . text overlap with arXiv:2310.11506 Subjects: Artificial Intelligence (cs.AI) ; Logic in Computer Science (cs.LO math.LO) Cite as: arXiv:2602.23302 [cs.AI] (or arXiv:2602.23302v1 [cs.AI] for this version) https://doi.org/10.48550/arXiv.2602.23302 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Giacomo Bonanno [ view email ] [v1] Thu, 26 Feb 2026 18:09:02 UTC (21 KB) Full-text links: Access Paper: 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 TeX Source view license Current browse context: cs.AI < prev | next > new | recent ...
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