Nonlinear Lie derivations of incidence algebras of finite rank

Let be a finite preordered set, R a 2-torsion free commutative ring with unity and the incidence algebra of X over R. In this paper we prove that every nonlinear Lie derivation of is of the standard form. More explicitly, each nonlinear Lie derivation of is a sum of an inner derivation, a transitive induced derivation, an additive induced derivation and a central-valued map.