On Mixed Iterated Revisions

TL;DR

This paper analyzes various iterable belief change operators, showing they can be reduced to three core types, and provides algorithms and complexity analysis for mixed sequences of belief revisions.

Contribution

It demonstrates all ten belief change operators can be reduced to three core types and offers an algorithm for restructuring sequences without explicit rewriting.

Findings

All ten operators are reducible to lexicographic revision, refinement, and severe withdrawal.

An algorithm is provided to restructure sequences without explicit rewriting.

Most belief change sequences require only polynomial calls to a satisfiability checker.

Abstract

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.