A Bipolar Possibilistic Representation of Knowledge and Preferences and Its Applications

When representing knowledge, it may be fruitful to distinguish between negative and positive information in the following sense. There are pieces of information ruling out what is known as impossible on the one hand, and pieces of evidence pointing out things that are guaranteed to be possible. But what is not impossible is not necessarily guaranteed to be possible. This applies as well to the modelling of the preferences of an agent when some potential choices are rejected since they are rather unacceptable, while others are indeed really satisfactory if they are available, leaving room for alternatives to which the agent is indifferent. The combination of negative information is basically conjunctive (as done classically in logic), while it is disjunctive in the case of positive information, which is cumulative by nature. This second type of information has been largely neglected by the logical tradition. Both types may be pervaded with uncertainty when modelling knowledge, or may be a matter of degree when handling preferences. The presentation will first describe how the two types of information can be accommodated in the framework of possibility theory. The existence of the two types of information can shed new light on the revision of a knowledge / preference base when receiving new information. It is also highly relevant when reasoning with (fuzzy) if-then rules, or for improving the expressivity of flexible queries.