Focusing vs. revision in possibility theory

Possibility measures are viewed as upper bounds of ill-known probabilities. More precisely, it is recalled that a possibility distribution is a faithful encoding of a set of lower bounds of probabilities bearing on a nested collection of subsets. Then two kinds of conditioning can be envisaged in this framework, namely revision and focusing. On the one hand, revision by a sure event A corresponds to adding a constraint enforcing that `not A´ is impossible, to the family of probability constraints. On the other hand, focusing amounts to a sensitivity analysis on the family of probability measures (induced by the lower bound constraints) once they are conditioned by A. When focusing on a particular situation A, the generic knowledge encoded by the family of probability measures induced by the lower bounds, is applied to this situation, without leading to a modification of the generic knowledge (which contrasts with revision where the generic knowledge is modified by the new constraint). Remarkably enough, focusing applied to a possibility measure yields a possibility measure again, which means that the conditioning of a family of probabilities, induced by lower bounds bearing on probabilities of nested events, can be faithfully handled on the possibility representation itself. Relations with results in the belief function setting are pointed out, as well as the difference between revision and focusing in possibility theory (interpreted as a probability bounds system)