  A general construction of an sh Lie algebra from a homological resolution of
a Lie algebra is given. It is applied to the space of local functionals
equipped with a Poisson bracket, induced by a bracket for local functions along
the lines suggested by Gel'fand, Dickey and Dorfman. In this way, higher order
maps are constructed which combine to form an sh Lie algebra on the graded
differential algebra of horizontal forms. The same construction applies for
graded brackets in field theory such as the Batalin-Fradkin-Vilkovisky bracket
of the Hamiltonian BRST theory or the Batalin-Vilkovisky antibracket.
