Ordinal Conditional Functions: A Dynamic Theory of Epistemic States

It is natural and important to have a formal representation of (plain) belief, according to which propositions are held true, or held false, or neither. And it is important to have a dynamic account of belief (section 1.1). AGM belief revision theory seems to provide such an account (section 1.2), but it founders at the problem of iterated belief revision, since it can generally account only for one step of revision. The paper discusses and rejects two solutions within the confines of AGM theory (section 1.3). It then introduces ordinal conditional functions (OCFs), now called ranking functions, as a solution of the problem (section 1.4), proposes general rules of belief change (in close analogy to Jeffrey’s generalized probabilistic conditionalization) that encompass revision and contraction as conceived in AGM theory (section 1.5), and proves that conditional independence w.r.t. OCFs satisfies the so-called graphoid axioms (section 1.6). The amazing parallel to probability theory is discussed in section 1.7. Section 1.8 concludes with a number of comparative remarks.