A belief revision framework for revising epistemic states with partial epistemic states

Belief revision performs belief change on an agent's beliefs when new evidence (either of the form of a propositional formula or of the form of a total pre-order on a set of interpretations) is received. Jeffrey's rule is commonly used for revising probabilistic epistemic states when new information is probabilistically uncertain. In this paper, we propose a general epistemic revision framework where new evidence is of the form of a partial epistemic state. Our framework extends Jeffrey's rule with uncertain inputs and covers well-known existing frameworks such as ordinal conditional function (OCF) or possibility theory. We then define a set of postulates that such revision operators shall satisfy and establish representation theorems to characterize those postulates. We show that these postulates reveal common characteristics of various existing revision strategies and are satisfied by OCF conditionalization, Jeffrey's rule of conditioning and possibility conditionalization. Furthermore, when reducing to the belief revision situation, our postulates can induce Darwiche and Pearl's postulates C1 and C2.