AGM Postulates in Arbitrary Logics: Initial Results and Applications

The problem of belief change refers to the updating of a Knowledge Base (KB) in the face of new, possibly contradictory information. The AGM theory, introduced in [1], is the dominating paradigm in the area of belief change. Unfortunately, the assumptions made by the authors of [1] in the formulation of their theory restrict its use to a specific class of logics. In this report, we investigate the possibility of extending their framework in a wider class of formalisms by examining the applicability of the AGM postulates in logics originally excluded from the AGM model. We conclude that in the wider class that we consider there are logics which do not admit AGM-compliant operators. As a case study, we investigate the applicability of the AGM theory to Description Logics (DLs). Furthermore, we use our results to shed light on our inability to develop AGM-compliant operators for belief bases.