Lack of Finite Characterizations for the Distance-based Revision

Lehmann, Magidor, and Schlechta developed an approach to belief revision based on distances between any two valuations. Suppose we are given such a distance D. This defines an operator |D, called a distance operator, which transforms any two sets of valuations V and W into the set V |D W of all elements of W that are closest to V. This operator |D defines naturally the revision of K by A as the set of all formulas satisfied in M(K) |D M(A) (i.e. those models of A that are closest to the models of K). This constitutes a distance-based revision operator. Lehmann et al. characterized families of them using a loop condition of arbitrarily big size. An interesting question is whether this loop condition can be replaced by a finite one. Extending the results of Schlechta, we will provide elements of negative answer. In fact, we will show that for families of distance operators, there is no "normal" characterization. Approximatively, a normal characterization contains only finite and universally quantified conditions. These results have an interest of their own for they help to understand the limits of what is possible in this area. Now, we are quite confident that this work can be continued to show similar impossibility results for distance-based revision operators, which suggests that the big loop condition cannot be simplified

Points de vue sur les croyances et leur changement

In this thesis, we propose logical models for belief representation and belief change in a multi-agent setting, stressing the importance of choosing a particular modeling point of view. In that respect, we distinguish two approaches: the external approach, where the modeler is somebody external to the situation; the internal approach, where the modeler is one of the agents. We propose an internal version of dynamic epistemic logic (with event models) which allows us to generalize easily AGM belief revision theory to the multi-agent case. Afterwards, we model the complex logical dynamics underlying the interpretation of events by adding probabilities and infinitesimals. Finally we propose an alternative without using event models by introducing instead a converse event operator.Dans cette thèse, nous proposons des modèles logiques pour la représentation des croyances et leur changement dans un cadre multi-agent, en insistant sur l'importance de se fixer un point de vue particulier pour la modélisation. A cet égard, nous distinguons deux approches différentes: l'approche externe, où le modélisateur est quelqu'un d'externe à la situation; l'approche interne, où le modélisateur est l'un des agents. Nous proposons une version interne de la logique épistémique dynamique (avec des modèles d'événements), ce qui nous permet de généraliser facilement la théorie de la révision des croyances d'AGM au cas multi-agent. Ensuite, nous mod´elisons les dynamismes logiques complexes qui soustendent notre interprétation des événements en introduisant des probabilités et des infinitésimaux. Finalement, nous proposons un formalisme alternatif qui n'utilise pas de modèle d'événement mais qui introduit à la place un opérateur d'événement inverse