Belief revision and update, two significant types of belief change, both focus on how an agent modify her beliefs in presence of new information. The most striking difference between them is that the former studies the change of beliefs in a static world while the latter concentrates on a dynamically-changing world. The famous AGM and KM postulates were proposed to capture rational belief revision and update, respectively. However, both of them are too permissive to exclude some unreasonable changes in the iteration. In response to this weakness, the DP postulates and its extensions for iterated belief revision were presented. Furthermore, Rodrigues integrated these postulates in belief update. Unfortunately, his approach does not meet the basic requirement of iterated belief update. This paper is intended to solve this problem of Rodrigues's approach. Firstly, we present a modification of the original KM postulates based on belief states. Subsequently, we migrate several well-known postulates for iterated belief revision to iterated belief update. Moreover, we provide the exact semantic characterizations based on partial preorders for each of the proposed postulates. Finally, we analyze the compatibility between the above iterated postulates and the KM postulates for belief update.

We focus on handling conflicting and uncertain information in lightweight ontologies, where uncertainty is represented in a possibilistic logic setting. We use DL-Lite, a tractable fragment of Description Logic, to specify terminological knowledge (i.e., TBox). We assume the TBox to be stable and coherent, while its combination with a set of assertional facts (i.e., ABox) may be inconsistent. We address the problem of dealing with conflicts when the reliability relation between sources is only partially ordered. We propose to represent the uncertain ABox as a symbolic weighted base, where a strict partial preorder is applied on the weights.

Because preferences naturally arise and play an important role in many real-life decisions, they are at the backbone of various fields. In particular preferences are increasingly used in almost all matching procedures-based applications. In this work we highlight the benefit of using AI insights on preferences in a large scale application, namely the French Admission Post-Baccalaureat Platform (APB). Each year APB allocates hundreds of thousands first year applicants to universities. This is done automatically by matching applicants preferences to university seats. In practice, APB can be unable to distinguish between applicants which leads to the introduction of random selection. This has created frustration in the French public since randomness, even used as a last mean does not fare well with the republican egalitarian principle. In this work, we provide a solution to this problem. We take advantage of recent AI Preferences Theory results to show how to enhance APB in order to improve expressiveness of applicants preferences and reduce their exposure to random decisions.

For instance, does it form a "nice" class, which can be characterized A formal framework is given for the postulate characterizability by postulates? of a class of belief revision operators, Proving non-characterizability presupposes a formal definition obtained from a class of partial preorders using of a postulate. However, as noted in the survey [Fermé minimization. It is shown that for classes of posets and Hansson, 2011] characterizability is equivalent to a special kind of "theories of belief change developed in the AGM definability in monadic second-order logic, which tradition are not logics in a strict sense, but rather turns out to be incomparable to first-order definability.

Starting with a likelihood or preference order on worlds, we extend it to a likelihood ordering on sets of worlds in a natural way, and examine the resulting logic. Lewis (1973) earlier considered such a notion of relative likelihood in the context of studying counterfactuals, but he assumed a total preference order on worlds. Complications arise when examining partial orders that are not present for total orders. There are subtleties involving the exact approach to lifting the order on worlds to an order on sets of worlds. In addition, the axiomatization of the logic of relative likelihood in the case of partial orders gives insight into the connection between relative likelihood and default reasoning.

A formal framework is given for the characterizability of a class of belief revision operators, defined using minimization over a class of partial preorders, by postulates. It is shown that for partial orders characterizability implies a definability property of the class of partial orders in monadic second-order logic. Based on a non-definability result for a class of partial orders, an example is given of a non-characterizable class of revision operators. This appears to be the first non-characterizability result in belief revision.

One of Judea Pearl's many, many important contributions to the study of causality was the first attempt to use the mathematical tools of causal modeling to give an account of "actual causation", a notion that has been of considerable interest among philosophers and legal theorists (Pearl, 2000, Chapter 10). Pearl later revised his account of actual causation in joint work with Halpern (Halpern & Pearl, 2005). A number of authors (Hall, 2007; Halpern, 2008; Hitchcock, 2007; Menzies, 2004) have suggested that an account of actual causation must be sensitive to considerations of normality, as well as to causal structure. In (Halpern & Hitchcock, 2011), we suggest a way of incorporating considerations of normality into the Halpern-Pearl theory, and show how to extend the account to illuminate features of the psychology of causal judgment, as well as features of causal reasoning in the law. Our account of actual causation makes use of "extended causal models", which include both structural equations among a set of variables, and a partial preorder on possible worlds, which represents the relative "normality" of those worlds. We actually want to think of people as working with the structural equations and normality order to evaluate actual causation. However, consideration of even simple examples immediately suggests a problem. A direct representation of the equations and normality order is too cumbersome for cognitively limited agents to use effectively. If our account of actual causation is to be at all realistic as a model of human causal judgment, some form of compact representation will be needed.