We look at iterated non-prioritised belief revision, using as a starting point a model of non-prioritised revision, similar to Makinson's screened revision, which assumes an agent keeps a set of core beliefs whose function is to block certain revision inputs. We study postulates for the iteration of this operation. These postulates generalise some of those which have previously been proposed for iterated AGM ("prioritised") revision, including those of Darwiche and Pearl. We then add a second type of revision operation which allows the core itself to be revised. Postulates for the iteration of this operator are also provided, as are rules governing mixed sequences of revisions consisting of both regular and core inputs. Finally we give a construction of both a regular and core revision operator based on an agent's revision history. This construction is shown to satisfy most of the postulates.
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