Incomparability and incommensurability in reasoning and belief dynamics
- Sylvain Lagrue
- HDR Defended on :
- Dec 12, 2011 • salle des thèses, Faculté des sciences Jean Perrin
Located in the field of Artificial Intelligence, our work revolves around two major unifying research themes: reasoning from uncertain beliefs and their dynamics. We are particularly interested in the management of incomparability and incommensurability problems that can arise when trying to manage information from highly heterogeneous sources.
We are first interested in reasoning in the presence of inconsistencies, from a purely ordinal point of view as well as from a more numerical point of view. In this first case, we propose and study different generalizations of well known reasoning methods, but focusing on totally ordered formulas. These generalizations allow to handle incomparabilities. In a more numerical framework, we have extended possibilistic logic in order to allow the representation of uncertainty associated to information using intervals. We have also proposed different methods to improve the productivity of inferences based on penalty logic by avoiding collisions.
Concerning the dynamics of beliefs, we have proposed a new set of postulates allowing to revise epistemic states represented by partial preorders. We present different operators verifying them as well as a representation theorem. We are also interested in the generalization of the fusion process in the case where agents do not share a unique scale and where the weights they provide are incommensurable. We propose different operators to model this process, their logical study, and an impossibility theorem.
Finally, we empirically study decision making in a non-deterministic and stochastic universe using a recent dice game, Pickomino.
Keywords: knowledge representation, belief dynamics, inconsistency management, incommensurability, incomparability, fusion, revision, Pickomino
- Philippe Besnard (Director of research CNRS IRIT)
- Ramón Pino-Pérez (Professor at the Universidad de Los Andes, Venezuela)
- Lluís Godo Lacasa (Research Professor at the Artificial Intelligence Research Institute (IIIA), Spain)
- Salem Benferhat (Professor at the University of Artois)
- Tristan Cazenave (Professor at the University of Paris-Dauphine)
- Éric Grégoire (Professor at the University of Artois)
- Pierre Marquis (Professor at the University of Artois)
- Odile Papini (Professor at the University of Aix-Marseille)