Ordinal and absolute representations of positive information in possibilistic logic

There are two readings of a possibility distribution, a representation format which is useful for encoding uncertain knowledge or preferences. The negative information reading, based on possibility and necessity measures, emphasizes the fact that some interpretations are impossible, or at least have an upper-bounded possibility level. The positive information reading points out that possibility degrees are lower bounded, and thus that some interpretations have non-zero (guaranteed) possibility degrees. This paper provides technical results for the positive view, showing how sets of absolute, or relative, constraints expressed in terms of guaranteed possibility measures can be represented in terms of a possibility distribution. Using previously obtained results for the “negative interpretation side”, it enables us to jointly handle upper and lower logical specifications of a possibility distribution on partitions of the set of interpretations, as pointed out in the