Bipolar Possibilistic Representations
  Recently, it has been emphasized that the possibility theory framework allows
us to distinguish between i) what is possible because it is not ruled out by
the available knowledge, and ii) what is possible for sure. This distinction
may be useful when representing knowledge, for modelling values which are not
impossible because they are consistent with the available knowledge on the one
hand, and values guaranteed to be possible because reported from observations
on the other hand. It is also of interest when expressing preferences, to point
out values which are positively desired among those which are not rejected.
This distinction can be encoded by two types of constraints expressed in terms
of necessity measures and in terms of guaranteed possibility functions, which
induce a pair of possibility distributions at the semantic level. A consistency
condition should ensure that what is claimed to be guaranteed as possible is
indeed not impossible. The present paper investigates the representation of
this bipolar view, including the case when it is stated by means of conditional
measures, or by means of comparative context-dependent constraints. The
interest of this bipolar framework, which has been recently stressed for
expressing preferences, is also pointed out in the representation of diagnostic
knowledge.
