Bridging Logical, Comparative, and Graphical Possibilistic Representation Frameworks

Possibility theory offers a qualitative framework for representing uncertain knowledge or prioritized desires. A remarkable feature of this framework is the existence of three distinct compact representation formats which are all semantically equivalent to a ranking of possible worlds encoded by a possibility distribution. These formats are respectively: i) a set of weighted propositional formulas; ii) a set of strict comparative possibility statements of the form "p is more possible than q", and iii) a directed acyclic graph where links are weighted by possibility degrees (either qualitative or quantitative). This paper exhibits the direct translation between these formats without resorting to a semantical (exponential) computation at the possibility distribution level. These translations are useful for fusing heterogenous information, and are necessary for taking advantages of the merits of each format at the representational or at the inferential level.