Current Research Trends in Possibilistic Logic: Multiple Agent Reasoning, Preference Representation, and Uncertain Databases

Possibilistic logic is a weighted logic that handles uncertainty, or preferences, in a qualitative way by associating certainty, or priority levels, to classical logic formulas. Moreover, possibilistic logic copes with inconsistency by taking advantage of the stratification of the set of formulas induced by the associated levels. Since its introduction in the mid-eighties, multiple facets of possibilistic logic have been laid bare and various applications addressed: handling exceptions in default reasoning, modeling belief revision, providing a graphical Bayesian-like network representation counterpart to a possibilistic logic base, representing positive and negative information in a bipolar setting with applications to preferences fusion and to version space learning, extending possibilistic logic for dealing with time, or multiple agents mutual beliefs, developing a symbolic treatment of priorities for handling partial orders between levels and also improving computational efficiency, learning stratified hypotheses for coping with exceptions. The chapter aims primarily at offering an introductory survey of possibilistic logic developments. Still, it also outlines new research trends that are relevant in preference representation, or in reasoning about epistemic states.