 Let \(\Pi(\mathcal{A})\) be the set of equivalence classes of \(\mathcal{A}\)-events under perspectivity, and denote the equivalence class of an event \(A\) by \(p(A)\); we then have a natural partial binary operation on \(\Pi(\mathcal{A})\) defined by \(p(A)\oplus p(B) = p(A\cup B)\) for orthogonal events \(A\) and \(B\). Setting 0 :\(= p(\varnothing)\) and 1 :\(= p(E), E\) any member of \(\mathcal{A}\), we obtain a partial-algebraic structure \((\Pi(\mathcal{A}),\oplus ,0,1)\), called the logic of \(\mathcal{A}\). This satisfies the following conditions: