Strictly locally order affine complete lattices

We call a latticeL strictly locally order-affine complete if, given a finite subsemilatticeS ofL ⁿ, every functionf: S L which preserves congruences and order, is a polynomial function. The main results are the following: (1) all relatively complemented lattices are strictly locally order-affine complete; (2) a finite modular lattice is strictly locally order-affine complete if and only if it is relatively complemented. These results extend and generalize the earlier results of D. Dorninger 2] and R. Wille 9, 10].