Let \({{{\mathcal {S}}}}({\mathcal {H}})\) denote the set of all self-adjoint operators (not necessarily bounded) on a Hilbert space \({\mathcal {H}}\), which is the set of all physical quantities on a quantum system \({\mathcal {H}}\). We introduce a binary relation \(\bot \) on \({{{\mathcal {S}}}}({\mathcal {H}})\). We show that if \(A\bot B\), then A and B are affiliated with some abelian von Neumann algebra. The relation \(\bot \) induces a partial algebraic operation \(\oplus \) on \({{{\mathcal {S}}}}({\mathcal {H}})\). We prove that \(({{{\mathcal {S}}}}({{\mathcal {H}}}), \bot , \oplus , 0)\) is a generalized orthoalgebra. This algebra is a generalization of the famous Birkhoff–von Neumann quantum logic model. It establishes a mathematical structure on all physical quantities on \({\mathcal {H}}\). In particular, we note that \((\mathcal{S}({{\mathcal {H}}}), \bot , \oplus , 0)\) has a partial order \(\preceq \), and prove that \(A\preceq B\) if and only if A has a value in \(\Delta \) implies that B has a value in \(\Delta \) for every Borel set \(\Delta \) not containing 0. Moreover, the existence of the infimum \(A\wedge B\) and supremum \(A\vee B\) for \(A,B\in {\mathcal {S}}({\mathcal {H}})\) (with respect to \(\preceq \)) is studied, and it is shown at the end that the position operator Q and momentum operator P in the Heisenberg commutation relation satisfy \(Q\wedge P=0\).