Belief Change and Semiorders

A central result in the AGM framework for belief revision is the construction of revision functions in terms of total preorders on possible worlds. These preorders encode comparative plausibility: r ă r1 states that the world r is at least as plausible as r1. Indifference in the plausibility of two worlds, r, r1, denoted r „ r1, is defined as r ⊀ r1 and r1 ⊀ r. Herein we take a closer look at plausibility indifference. We contend that the transitivity of indifference assumed in the AGM framework is not always a desirable property for comparative plausibility. Our argument originates from similar concerns in preference modelling, where a structure weaker than a total preorder, called a semiorder, is widely consider to be a more adequate model of preference. In this paper we essentially re-construct revision functions using semiorders instead of total preorders. We formulate postulates to characterise this new, wider, class of revision functions, and prove that the postulates are sound and complete with respect to the semiorder-based construction. The corresponding class of contraction functions (via the Levi and Harper Identities) is also characterised