We investigate supersymmetric models where neither R parity nor lepton numb
er nor baryon number is imposed. The full high energy theory has an exact h
orizontal U(1) symmetry that is spontaneously broken. Quarks and Higgs fiel
ds carry integer horizontal charges but leptons carry half integer charges.
Consequently, the effective low energy theory has two special features: a
U(1) symmetry that is explicitly broken by a small parameter, leading to se
lection rules, and an exact residual Z(2) symmetry, that is lepton parity.
As concerns neutrino parameters, the Z(2) symmetry forbids contributions fr
om R-p-violating couplings and the U(1) symmetry induces the required hiera
rchy. As concerns baryon number violation, the Z(2) symmetry forbids proton
decay and the U(1) symmetry provides sufficient suppression of double nucl
eon decay and of neutron antineutron oscillations.