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A universal formulation of uncertainty relations for quantum measurements ispresented with additional focus on the representability of quantum observablesby classical observables over a given state. Owing to the simplicity andoperational tangibility of the framework, the resultant general relations admitnatural operational interpretations and characterisations, and are thus alsoexperimentally verifiable. In view of the universal formulation, Heisenberg'sphilosophy of the uncertainty principle is also revisited; it is reformulatedand restated as a refined no-go theorem, albeit perhaps in a weaker form thanwas originally intended. In fact, the relations entail, in essence ascorollaries to their special cases, several previously known relations,including most notably the Arthurs-Kelly-Goodman, Ozawa, andWatanabe-Sagawa-Ueda relations for quantum measurements. The Schr{\"o}dingerrelation (hence the standard Kennard-Robertson relation as its trivialcorollary as well) is also shown to be a special case when the measurement isnon-informative.

A Universal Formulation of Uncertainty Relation for Errors under Local Representability