Non-Prioritized Iterated Revision: Improvement via Incremental Belief Merging

Abstract : In this work we define iterated change operators that do not obey the primacy of update principle. This kind of change is required in applications when the recency of the input formulae is not linked with their reliability/priority/weight. This can be translated by a commutativity postulate that asks the result of a sequence of changes to be the same whatever the order of the formulae of this sequence. Technically then we end up with a sequence of formulae that we have to combine in order to obtain a meaningful belief base. Belief merging operators are then natural candidates for this task. We show that we can define improvement operators using an incremental belief merging approach. We also show that these operators can not be encoded as simple preorders transformations, contrary to most iterated revision and improvement operators.