Graphical readings of possibilistic logic bases

Possibility theory offers either a qualitive, or a numerical framework for representing uncertainty, in terms of dual measures of possibility and necessity. This leads to the existence of two kinds of possibilistic causal graphs where the conditioning is either based on the minimum, or the product operator. Benferhat et al. (1999) have investigated the connections between min-based graphs and possibilistic logic bases (made of classical formulas weighted in terms of certainty). This paper deals with a more difficult issue : the product-based graphical representations of possibilistic bases, which provides an easy structural reading of possibilistic bases. Moreover, this paper also provides another reading of possibilistic bases in terms of comparative preferences of the form "in the context p, q is preferred to not q". This enables us to explicit preferences underlying a set of goals with different levels of priority.