Orthomodular lattice

Summary

An orthomodular lattice is an orthocomplemented lattice that satisfies the orthomodular law: if $a \le b$, then $b = a \vee (a^\perp \wedge b)$. The lattice of closed subspaces of any Hilbert space is orthomodular, even when it is not modular. Every Boolean algebra and every modular ortholattice is orthomodular. Orthomodular lattices are the standard algebraic model of the propositions of quantum logic.