Belief Change and Semiorders

ABSTRACT. 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 <= r' states that the world r is at least as plausible as r'. Indifference in plausibility, denoted r ~ r', is defined as r ~ r' iff r <= r' and r' <= r. Herein we take a closer look at plausibility indifference. We contend that the transitivity of indifference assumed in the AGM framework is not, in general, an intuitive 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 postulate to characterise this new, wider, class of revision functions, and prove that the postulates are soundness and completeness with respect to the semiorders-based construction. Moreover, through the Levi and Harper Identities, we characterise axiomatically the corresponding class of contraction functions.