In the last decade, AI researchers have pointed out the existence of two types of information: positive information and negative information. This distinction has also been asserted in cognitive psychology. Distinguishing between these two types of information may be useful in both knowledge and preference representation. In the first case, one distinguishes between situations which are not impossible because they are not ruled out by the available knowledge, and what is possible for sure. In the second case, one distinguishes between what is not rejected and what is really desired. Besides it has been shown that possibility theory is a convenient tool to model and distinguish between these two types of information. Knowledge/Preference representation languages have also been extended to cope with this particular kind of information. Nevertheless despite solid theoretical advances in this topic, the crucial question of ''which reading (negative or positive) one should have'' remains a real bottleneck. In this paper, we focus on comparative statements. We present a set of postulates describing different situations one may encounter. Then we provide a representation theorem describing which sets of postulates are satisfied by which kind of information (negative or positive) and conversely. One can then decide which reading to apply depending on which postulates she privileges.