  In this paper we show that several classes of partially ordered structures
having paraorthomodular reducts, or whose sections may be regarded as
paraorthomodular posets, admit a quite natural notion of implication, that
admits a suitable notion of adjointness. Within this framework, we propose a
smooth generalization of celebrated Greechie's theorems on amalgams of finite
Boolean algebras to the realm of Kleene lattices.
