  We show that in the minimal three generation seesaw models for neutrinos, the
presence of leptonic $(L_e+L_{\mu}-L_{\tau})\times S_2$ symmetry leads to one
of the right handed neutrinos remaining massless. This state can then be
identified with the sterile neutrino required for a simultaneous understanding
of solar, atmospheric and LSND observations. We present a gauge model where the
presence of higher dimensional operators originating from Planck scale physics
lead to a realistic 2+2 mixed scenario that fits all oscillation data. The
model predicts a range for the mixing angle $U_{e3}$ and an effective mass for
neutrinos emitted in tritium decay, which can be used to test this model.
