 Associated with any probabilistic model \((\mathcal{A},\Delta)\) are several partially ordered sets, each of which has some claim to the status of an “empirical logic” associated with the model. In this section, I’ll discuss two: the so-called operational logic \(\Pi(\mathcal{A})\) and the property lattice \(\mathbf{L}(\mathcal{A},\Delta)\). Under relatively benign conditions on \(\mathcal{A}\), the former is an orthoalgebra. The latter is always a complete lattice, and under plausible further assumptions, atomic. Moreover, there is a natural order preserving mapping from \(\Pi\) to \(\mathbf{L}\). This is not generally an order-isomorphism, but when it is, we obtain a complete orthomodular lattice, and thus come a step closer to the projection lattice of a Hilbert space. 