  It is shown that propositional calculuses of both quantum and classical
logics are non-categorical. We find that quantum logic is in addition to an
orthomodular lattice also modeled by a weakly orthomodular lattice and that
classical logic is in addition to a Boolean algebra also modeled by a weakly
distributive lattice. Both new models turn out to be non-orthomodular. We prove
the soundness and completeness of the calculuses for the models. We also prove
that all the operations in an orthomodular lattice are five-fold defined. In
the end we discuss possible repercussions of our results to quantum
computations and quantum computers.
