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.

翻译：针对KM信念更新的每一条公理，我们在一类包含三个模态算子的模态逻辑中给出了对应的公理：一个单模态信念算子$B$、一个双模态条件算子$>$以及单模态必然算子$\square$。随后，我们将所得逻辑与通过将AGM信念修正公理转化为模态公理而得到的类似逻辑进行比较，并证明后者包含前者。记后者为$\mathcal L_{AGM}$，前者为$\mathcal L_{KM}$，我们证明$\mathcal L_{KM}$的每一条公理都是$\mathcal L_{AGM}$的定理。因此，AGM信念修正可视为KM信念更新的特例。对于KM信念更新的强版本，我们证明$\mathcal L_{KM}$与$\mathcal L_{AGM}$之间的差异可归结为一条单独的公理，该公理专门处理非意外信息，即那些初始并未被否定的公式。