  We show that well-chosen Lagrangians for a class of two-dimensional
integrable lattice equations obey a closure relation when embedded in a higher
dimensional lattice. On the basis of this property we formulate a Lagrangian
description for such systems in terms of Lagrangian multiforms. We discuss the
connection of this formalism with the notion of multidimensional consistency,
and the role of the lattice from the point of view of the relevant variational
principle.
