  It has recently been discovered that both quantum and classical propositional
logics can be modelled by classes of non-orthomodular and thus non-distributive
lattices that properly contain standard orthomodular and Boolean classes,
respectively. In this paper we prove that these logics are complete even for
those classes of the former lattices from which the standard orthomodular
lattices and Boolean algebras are excluded. We also show that neither quantum
nor classical computers can be founded on the latter models. It follows that
logics are "valuation-nonmonotonic" in the sense that their possible models
(corresponding to their possible hardware implementations) and the valuations
for them drastically change when we add new conditions to their defining
conditions. These valuations can even be completely separated by putting them
into disjoint lattice classes by a technique presented in the paper.
