About the dynamics of iterated knowledge fusion by weakening

One of the main issues about logic-oriented knowledge fusion concerns the way contradictory information should be handled. Many syntax-based approaches require some information to be dropped in case of logical inconsistency. On the contrary, the technique described in the paper simply weakens some information to overcome inconsistency. A family of fusion approaches is presented, encompassing various inconsistency handling policies. They basically adopt an unbiased position with respect to two knowledge sources in the sense that they do not make one source predominate the other one. However, enforcing a preference for one source and retracting this preference is easy. When the fusion process is iterated, it is shown that the approaches can lead sources to be rejected. Conditions preventing such a drawback are investigated. It is also shown how this problem can be solved when all sources are available simultaneously. Finally, a preference for less-contradicted sources is characterized in this framework.