Quantum theory as a theory in a classical propositional calculus

Classical logic and Boolean algebras are, of course, very intimately related. It is, however, possible to show that lattices of propositions isomorphic to the lattice of all the closed subspaces of a separable Hilbert space arise quite naturally within the classical propositional logic. This was first shown by the author in 1987 in connection with a certain type of theories calledtheories with orthocomplementation. These theories are not easy to interpret physically and it is shown that simpler theories, which are more amenable to physical interpretation, can also be used. It is then possible to assume that quantum theory is such a theory and, as a result, to formulate a new approach that provides a way of looking at the wave-particle duality and touches upon the foundations of quantum field theory.