On Mixed Iterated Revisions
  Several forms of iterable belief change exist, differing in the kind of
change and its strength: some operators introduce formulae, others remove them;
some add formulae unconditionally, others only as additions to the previous
beliefs; some only relative to the current situation, others in all possible
cases. A sequence of changes may involve several of them: for example, the
first step is a revision, the second a contraction and the third a refinement
of the previous beliefs. The ten operators considered in this article are shown
to be all reducible to three: lexicographic revision, refinement and severe
withdrawal. In turn, these three can be expressed in terms of lexicographic
revision at the cost of restructuring the sequence. This restructuring needs
not to be done explicitly: an algorithm that works on the original sequence is
shown. The complexity of mixed sequences of belief change operators is also
analyzed. Most of them require only a polynomial number of calls to a
satisfiability checker, some are even easier.
