changed in response of a revision. While single-step revision is about how a knowledge base has to be changed into a new knowledge base , iterated revision is about how a preference ordering (representing both the current knowledge and how much situations believed to be false are considered possible) should be turned into a new preference relation when is learned. A single step of iterated revision produces a new ordering that allows for further revisions. Two kinds of preference ordering are usually considered: numerical and non-numerical. In the first case, the level of plausibility of a model is representing by a non-negative integer number; the lower the rank, the more plausible the situation corresponding to the model. Non-numerical preference orderings correspond to the preference relations used in the AGM framework: a possibly total ordering over models. The non-numerical preference relation were initially considered unsuitable for iterated revision because of the impossibility of reverting a revision by a number of other revisions, which is instead possible in the numerical case. Darwiche and Pearl formulated the following postulates for iterated revision. if then ; if , then ; if , then ; if , then . Specific iterated revision operators have been proposed by Spohn, Boutilier, Williams, Lehmann, and others. Williams also provided a general iterated revision operator. Spohn rejected revision this non-numerical proposal has been first considered by Spohn, who rejected it based on the fact that revisions can change some orderings in such a way the original ordering cannot be restored with a sequence of other revisions; this operator change a preference ordering in view of new information by making all models of being preferred over all other models; the original preference ordering is maintained when comparing two models that are both models of or both non-models of ; Natural revision while revising a preference ordering by a formula , all minimal models (according to the preference ordering) of are made more preferred by all other ones; the original ordering of models is preserved when comparing two models that are not minimal models of ; this operator changes the ordering among models minimally while preserving the property that the models of the knowledge base after revising by are the minimal models of according to the preference ordering; Transmutations Williams provided the first generalization of belief revision iteration using transmutations. She illustrated transmutations using two forms of revision, conditionalization and adjustment,