Iterated Revision in the Spirit of Update: A Lazy Update

Since they were introduced, AGM revision and Katsuno and Mendelzon's update have been considered orthogonal theory change operations serving diierent purposes. This work provides a new presentation of AGM revision based on the update semantic apparatus establishing in such a way a bridge between the two seemingly incomparable frameworks. We deene a new operation as a variant of the standard update that we call lazy update. We prove the correspondence between lazy updates and (transitively relational, well behaved) AGM revisions when a given xed theory is considered (Theorem 3.11). Furthermore, given that lazy update allows iteration, we can characterize lazy update functions as those AGM revisions satisfying (K*1)-(K*8) plus two new postulates (LU-9) and (LU-8) governing the revision of diierent theories (Theorem 4.3). We believe these results bring new light to the issue of how revision and update functions are related. They also provide a novel way to achieve iterated theory revision. 1 Overview Since they were introduced, the AGM notion of revision 1] and Katsuno and Mendelzon's update 5] have been considered two fundamentally diierent ways of changing knowledge. The usual interpretation is as follows Revision takes place when new information is regarded as correcting our theory of a static world. According to revision, as little as possible of the original theory should be changed in order to accommodate the new information. It is in this sense that revision involves minimal change. Update, in contrast, takes place when our knowledge is modiied in response to changes into an evolving world. When new information is confronted, each complete consistent extension of our theory about the world should be considered. From the perspective of each of these extensions, the most similar complete theory accounting for the new information should be chosen. The result of the update is what the new theories have in common. It is in this sense that update involves maximal similarity.