Relevant minimal change in belief update

The notion of relevance was introduced by Parikh in the belief revision field for handling minimal change. It prevents the loss of beliefs that do not have connections with the epistemic input. But, the problem of minimal change and relevance is still an open issue in belief update. In this paper, a new framework for handling minimal change and relevance in the context of belief update is introduced. This framework goes beyond relevance in Parikh's sense and enforces minimal change by first rewriting the Katzuno-Mendelzon postulates for belief update and second by introducing a new relevance postulate. We show that relevant minimal change can be characterized by setting agent's preferences on beliefs where preferences are indexed by subsets of models of the belief set. Each subset represents a prime implicant of the belief set and thus stresses the key propositional symbols for representing the belief set.