Yes, we have won promotion to the top division every so often; but the fact of promotion logically implies an earlier relegation.
For example, in order to show that a certain formula F logically implies another formula G, one tries to construct in step-by-step fashion a model of the logical system (i.e., an assignment of values to its names and predicates) in which F is true but G is false.
The idea of saving or delivering from some dire situation logically implies that humankind, as a whole or in part, is in such a situation.
The implication problem is the most important one in dependency theory, and is the problem of determining if a set of dependencies logically implies another dependency.
Deductively, e logically implies h if h is true in every model for e. Degree of confirmation is thus a metrical generalization of first-order logical implication.
Khayyam's achievement in this topic was not to invent a new definition, but rather to demonstrate that each of the existing definitions logically implies the other.
One might, for example, appeal to some closure principle about causal power, claiming that if A causes B and B logically implies C, then A causes C.
Google's claim against the German law logically implies that snippets of information are a necessary part of the search engine experience, aiding web surfers as they scour information for their investigatory needs.
Robustness of the phenotype to environmental perturbation logically implies that there must be variability, in the sense of "the ability to vary" at some underlying level [3], [11].
While the former logically implies a prohibition of the use of chainsaws, the latter condition is much less clearly understood.
