Partitioned Linear Orders and Belief Revision

Despite their expressive power in representing alternatives or beliefs tainted by incomparabilities, it is often difficult to use generic partial orders. Hence, various structures have been historically studied in the literature, such as weak orders, semiorders or interval orders, each capturing a different fragment of partial orders. In this article, we propose and study in detail a fragment rich enough to represent some highly intuitive patterns involving incomparable elements that cannot be captured by the aforementioned fragments: partitioned linear orders (PLOs). These structures can be viewed as split independent linear orders, each one of them representing a local totally ranked situation. Then, we show how they can be used in Katsuno-Mendelzon-style belief revision. We propose a set of postulates, a representation theorem and a family of concrete operators.