  Contrary to classical semantics, the disjunction of two experimental
propositions relating to pure states of a quantum system ("quantum
propositions" for short) can be true even in the case where neither disjunct is
true. This suggests that in such case either both disjuncts are false and so
the distributive laws are not applicable to quantum propositions (this
inference is accepted in quantum logic) or the disjuncts are not bivalent,
i.e., neither true nor false, therefore the principle of bivalence is not
applicable to quantum propositions. But, to accept the latter inference, one
must explain how quantum propositions become bivalent in the classical limit.
This paper shows the emergence of bivalence through the interaction between a
quantum system and its environment and compares the environmentally induced
bivalence with the classical limit of quantum logic.
