Forbidden configurations for distributive, modular and semidistributive posets

In this paper, we give characterizations for distributive, modular, semidistributive, semimodular, 00-distributive and 00-modular lattices using incomparability relations. We generalize these concepts to posets and call them ∥∥-distributive, ∥∥-modular, ∥∥-semidistributive, LULU-semimodular, 00-∥∥-distributive and 00-∥∥-modular posets and obtain forbidden configurations for these classes with finite length by means of LULU-subposets.