 Note that all the considerations relevant to the interpretation of Bayesian conditionalization (discussed in  Section 3.1.4)  apply equally to ranking-theoretic conditioning. It is clear from the definition of conditioning that, as in the Bayesian case, the rank of the material conditional is a lower bound for the conditional rank: \(\beta(A\rightarrow B)\leq \beta(B|A)\). That ensures that ranking-theoretic update satisfies Conditionalization ( see  Section 2.1.1).  It also satisfies a version of Rational Monotony: if \(\beta(\neg A)=0\) and \(\beta(B)&gt;0,\) then \(\beta(B|A)&gt;0.\) Therefore, ranking-theoretic update satisfies the “spirit” of AGM update. Note, however, that ranking theory has no trouble with iterated belief revision: a revision takes as input a ranking function and an evidential proposition and outputs a new ranking function. Moreveover, the situation changes if the threshold for belief is raised to some positive number greater than zero: in that case, Rational Monotony may no longer be satisfied (see Raidl, 2019). 