  We define a set of pseudo-observables characterizing the properties of Higgs
decays in generic extensions of the Standard Model with no new particles below
the Higgs mass. The pseudo-observables can be determined from experimental
data, providing a systematic generalization of the "kappa-framework" so far
adopted by the LHC experiments. The pseudo-observables are defined from
on-shell decay amplitudes, allow for a systematic inclusion of higher-order QED
and QCD corrections, and can be computed in any Effective Field Theory (EFT)
approach to Higgs physics. We analyze the reduction of the number of
independent pseudo-observables following from the hypotheses of
lepton-universality, CP invariance, custodial symmetry, and linearly realized
electroweak symmetry breaking. We outline the importance of kinematical studies
of $h\to 4\ell$ decays for the extraction of such parameters and present their
predictions in the linear EFT framework.
