  Let ${\cal S}(\mathcal{H})$ 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 ${\cal S}(\mathcal{H})$. 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 ${\cal
S}(\mathcal{H})$. We prove that $({\cal S}({\mathcal{H}}), \bot, \oplus, 0)$ 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 $({\cal S}({\mathcal{H}}), \bot, \oplus, 0)$ 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
$Q\wedge P=0$.
