Possibilistic logic bases and possibilistic graphs
  Possibilistic logic bases and possibilistic graphs are two different
frameworks of interest for representing knowledge. The former stratifies the
pieces of knowledge (expressed by logical formulas) according to their level of
certainty, while the latter exhibits relationships between variables. The two
types of representations are semantically equivalent when they lead to the same
possibility distribution (which rank-orders the possible interpretations). A
possibility distribution can be decomposed using a chain rule which may be
based on two different kinds of conditioning which exist in possibility theory
(one based on product in a numerical setting, one based on minimum operation in
a qualitative setting). These two types of conditioning induce two kinds of
possibilistic graphs. In both cases, a translation of these graphs into
possibilistic bases is provided. The converse translation from a possibilistic
knowledge base into a min-based graph is also described.
