The logic of KM belief update is contained in the logic of AGM belief revision

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 LAGM and the former by mathcal LKM we show that every axiom of mathcal LKM is a theorem of mathcal LAGM. 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 LKM and mathcal LAGM can be narrowed down to a single axiom, which deals exclusively with unsurprising information, that is, with formulas that were not initially disbelieved.