Model Transformations for Ranking Functions and Total Preorders

Abstract: In the field of knowledge representation, the considered epistemic states are often based on propositional interpretations, also called worlds. E.g., epistemic states of agents can be modelled by ranking functions or total preorders on worlds. However, there are usually different ways of how to describe a real world situation in a propositional language; this can be seen as different points of view on the same situation. In this paper we introduce the concept of model transformations to convert an epistemic state from one point of view to another point of view, yielding a novel notion of equivalence of epistemic states. We show how the well-known advantages of syntax splitting, originally developed for belief sets and later extended to representation of epistemic states and to nonmonotonic reasoning, can be exploited for belief revision via model transformation by uncovering splittings not being present before. Furthermore, we characterize situations where belief change operators commute with model transformations.