Belief Revision and Ordered Theory Presentations

The standard theory of belief revision|known as the AGM theory after its authors, C. Al-chourrr on, P. GG ardenfors and D. Makinson 3]|suuers from at least two disadvantages. One is that it represents belief states as innnite objects, namely deductively closed sets of sentences. Another is that existing belief revision models make too strong assumptions about what information is available to guide revisions. A consequence of this is that repeated revisions are impossible. In this paper, we show how to use ordered theory presentations to represent belief states 1. Ordered theory presentations are theory presentations equipped with a partial order. In this paper we are only concerned with a special case, in which the sets are nite and the order is total, or linear. We deene a revision operator, which is shown to satisfy some, but not all, of the AGM postulates. No information other than that encoded in the OTP is needed to eeect the revision; this makes repeated revision easy.