which work on numerical preference orderings; revision requires not only a formula but also a number or ranking of an existing belief indicating its degree of plausibility; while the preference ordering is still inverted (the lower a model, the most plausible it is) the degree of plausibility of a revising formula is direct (the higher the degree, the most believed the formula is); Ranked revision a ranked model, which is an assignment of non-negative integers to models, has to be specified at the beginning; this rank is similar to a preference ordering, but is not changed by revision; what is changed by a sequence of revisions are a current set of models (representing the current knowledge base) and a number called the rank of the sequence; since this number can only monotonically non-decrease, some sequences of revision lead to situations in which every further revision is performed as a full meet revision. Merging The assumption implicit in the revision operator is that the new piece of information is always to be considered more reliable than the old knowledge base . This is formalized by the second of the AGM postulates: is always believed after revising with . More generally, one can consider the process of merging several pieces of information (rather than just two) that might or might not have the same reliability. Revision becomes the particular instance of this process when a less reliable piece of information is merged with a more reliable . While the input to the revision process is a pair of formulae and , the input to merging is a multiset of formulae , , etc. The use of multisets is necessary as two sources to the merging process might be identical. When merging a number of knowledge bases with the same degree of plausibility, a distinction is made between arbitration and majority. This distinction depends on the assumption that is made about the information and how it has to be put together. Arbitration the result of arbitrating two knowledge bases and entails ; this condition formalizes the assumption of maintaining as much as the old information as possible, as it is equivalent to imposing that every formula entailed by both knowledge bases is also entailed by the result of their arbitration; in a possible world view, the "real" world is assumed one of the worlds considered possible according to at least one of the