 The characterization theorem implies that we can think of a reliable method as adopting internal strengthened versions of the original hypotheses under investigation that are refutable. As the example above shows, the theorem does not imply that the strengthened hypotheses are mutually exclusive (e.g.“at most 3 swans are black” is consistent with “at most 2 swans are black”.). A recent alternative characterization theorem due to Baltag, Gierasimczuk, and Smets [2015] provides an alternative structural analysis where identifiable hypotheses are decomposed into mutually exclusive components, as follows.