We present a bottom-up approach to hierarchical classification based on posteriors conditioned with logits. Beginning with the output logits for a set of terminal labels from a base classifier, an initial hypothesis is repeatedly generalized (softened) to a weaker label until a particular confidence measure is achieved. As conditioning the probabilistic model with the full set of terminal logits quickly becomes intractable for large label sets, we propose an alternative approach employing "generalized logits" spanning relevant hypotheses within the label hierarchy. Experimental results are compared with related methods on multiple datasets and base classifiers. The proposed approach provides an efficient and effective hierarchical classification framework with monotonic, non-decreasing inference behavior.