Directed possibilistic graphs and possibilistic logic

This paper presents a study of the links between two different kinds of knowledge representation frameworks: a Bayesian-like network representation and a logic-based representation, both in the setting of possibility theory. There are two definitions of the notion of conditioning in possibility theory, depending if we are using a numerical or a qualitative scale. These two definitions lead to defining two kinds of possibilistic networks. In both cases, a translation of these possibilistic Bayesian-like networks into possibilistic knowledge bases is possible. The converse translation from a possibilistic knowledge base into a possibilistic network is also briefly described.