Introduction

Abstract

In 1936, G. Birkhoff and J. v. Neumann published an article with the title ‘The logic of quantum mechanics’. In this paper, the authors demonstrated that in quantum mechanics the most simple observables which correspond to yes-no propositions about a quantum physical system constitute an algebraic structure, the most important properties of which are given by an orthocomplemented and quasimodular lattice L_q. Furthermore, this lattice of quantum mechanical propositions has, from a formal point of view, many similarities with a Boolean lattice L_B which is known to be the lattice of classical propositional logic. Therefore, one could conjecture that due to the algebraic structure of quantum mechanical observables a logical calculus Q of quantum mechanical propositions is established, which is slightly different from the calculus L of classical propositional logic but which is applicable to all quantum mechanical propositions (C.F. v. Weizsäcker, 1955). This calculus has sometimes been called ‘quantum logic’.