  We propose a semantic representation of the standard quantum logic QL within
a classical, normal modal logic, and this via a lattice-embedding of
orthomodular lattices into Boolean algebras with one modal operator. Thus our
classical logic is a completion of the quantum logic QL. In other words, we
refute Birkhoff and von Neumann's classic thesis that the logic (the formal
character) of Quantum Mechanics would be non-classical as well as Putnam's
thesis that quantum logic (of his kind) would be the correct logic for
propositional inference in general. The propositional logic of Quantum
Mechanics is modal but classical, and the correct logic for propositional
inference need not have an extroverted quantum character. One normal necessity
modality suffices to capture the subjectivity of observation in quantum
experiments, and this thanks to its failure to distribute over classical
disjunction. The key to our result is the translation of quantum negation as
classical negation of observability.
