 A condition related to, but stronger than, orthocoherence is that any pairwise compatible propositions should be jointly compatible. This is sometimes called regularity. Most naturally occurring orthomodular lattices and posets are regular. In particular, Harding (1996, 1998) has shown that the direct-product decompositions of any algebraic, relational or topological structure can be organized in a natural way into a regular orthomodular  poset.[12] 