Abstract
The quantum logical approach to quantum mechanics in Hilbert space presupposes value definiteness of elementary propositions. Although the description of the measurement process by sequential quantum logic seems to justify this precondition, it is found to be incompatible with the quantum theory of measurement, which does not provide the decoherence of pointer values. The attempts to solve the measurement problem by means of histories and by quantum gravity fail, since these approaches are based on sequential quantum logic and its preconditions, too. Finally, we discuss consequences of these results.
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