ADM Quasi-merging and Pure-arbitration∗

The present paper introduces two new information merging protocols for the family of adaptive logics ADM, for which majority merging has been defined in [19]. The new adaptive operators reflect the negotiation processes of quasi-merging and pure arbitration, known from the Integrity Constraints framework introduced in [13]. The Adaptive Variant Counting selection provides a result equivalent to the GMax family of merging operators: it selects a collective model for a multi-set of belief bases based on the number of disagreements verified by the various models according to a leximax function. The Adaptive Minimax Counting selection is a quasi-merging operator which applies a minimax function and it obtains a larger spectrum of possibilities than the previous selection: it simulates the behaviour of the Max family of operators from the Integrity Constraints framework, avoiding some of its counterintuitive results.