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 proper- ties of
which are given by an orthocomplemented and quasimodular lattice Lq.
Furthermore, this lattice of quantum mechanical proposi- tions has, from
a formal point of view, many similarities with a Boolean lattice L8
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. Weizsacker, 1955). This
calculus has sometimes been called 'quan- tum logic'. However, the
statement that propositions about quantum physical systems are governed
by the laws of quantum logic, which differ from ordinary classical logic
and which are based on the empirically well-established quantum theory,
is exposed to two serious objec- tions: (a) Logic is a theory which
deals with those relationships between various propositions that are
valid independent of the content of the respective propositions. Thus,
the validity of logical relationships is not restricted to a special
type of proposition, e. g. to propositions about classical physical
systems.
