Generalizing the AGM postulates: preliminary results and applications

One of the crucial actions any reasoning system must undertake is the updating of its Knowledge Base (KB). This problem is usually referred to as the problem of belief change. The AGM approach, introduced in (Alchourron, Gärdenfors, and Makinson 1985), is the dominating paradigm in the area but it makes some non-elementary assumptions about the logic at hand which disallow its direct application in some classes of logics. In this paper, we drop all such assumptions and determine the necessary and sufficient conditions for a logic to support AGMcompliant operators. Our approach is directly applicable to a much broader class of logics. We apply our results to establish connections between the problem of updating in Description Logics (DLs) and the AGM postulates. Finally, we investigate why belief base operators cannot satisfy the AGM postulates in standard logics.