On Mixed Iterated Revisions
This work addresses a foundational problem in belief revision for AI and logic, but it is incremental as it builds on existing operators and reduction methods.
The paper tackles the problem of handling sequences of mixed belief change operators by showing that ten operators can be reduced to three, and these can be expressed in terms of lexicographic revision with an algorithm that works on the original sequence, analyzing complexity to show most require only polynomial calls to a satisfiability checker.
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.