 Some version of orthocoherence or regularity was taken by Mackey and many of his successors as an axiom. (Orthocoherence appears, in an infinitary form, as Mackey’s axiom V; regularity appears in the definition of a partial Boolean algebra in the work of Kochen and Specker (1965).) However, it is quite easy to construct simple model test spaces, having perfectly straightforward—even classical—interpretations, the logics of which are not orthocoherent. There has never been given any entirely compelling reason for regarding orthocoherence as an essential feature of all reasonable physical models. Moreover, certain apparently quite well-motivated constructions that one wants to perform with test spaces tend to destroy orthocoherence (see  section 7).