 We now have two different “logics” associated with a probabilistic model \((\mathcal{A},\Delta)\) with \(\mathcal{A}\) algebraic: a “logic” \(\Pi(\mathcal{A})\) of experimental propositions that is an orthoalgebra, but generally not a lattice, and a “logic” \(\mathbf{L}(\mathcal{A},\Delta)\) of properties that is a complete lattice, but rarely orthocomplemented in any natural way (Randall and Foulis [1983]). The two are connected by a natural mapping [ ] : \(\Pi \rightarrow \mathbf{L}\), given by \(p \rightarrow[p] = F(J_p)\) where for each \(p\in \Pi\), \(J_p = \{x\in X \mid p(x) \nleq p' \}\). That is, \(J_p\) is the set of outcomes that are consistent with \(p\), and [\(p\)] is the largest (i.e., weakest) physical property making \(p\) certain to be confirmed if tested.