  We consider a proper propositional quantum logic and show that it has
multiple disjoint lattice models, only one of which is an orthomodular lattice
(algebra) underlying Hilbert (quantum) space. We give an equivalent proof for
the classical logic which turns out to have disjoint distributive and
non-distributive ortholattices as its models. In particular, we prove that both
classical and quantum logics are sound and complete with respect to each of
these lattices. We also show that there is one common non-orthomodular lattice
that is a model of both quantum and classical logics. In technical terms, that
enables us to run the same classical logic on both a digital (standard, two
subset, 0-1 bit) computer and on a non-digital (say, a six subset) computer
(with appropriate chips and circuits). With quantum logic, the same six element
common lattice can serve us as a benchmark for an efficient evaluation of
equations of bigger lattice models or theorems of the logic.
