  If a quantum system is prepared and later post-selected in certain states,
"paradoxical" predictions for intermediate measurements can be obtained. This
is the case both when the intermediate measurement is strong, i.e. a projective
measurement with Luders-von Neumann update rule, or with weak measurements
where they show up in anomalous weak values. Leifer and Spekkens
[quant-ph/0412178] identified a striking class of such paradoxes, known as
logical pre- and post-selection paradoxes, and showed that they are indirectly
connected with contextuality. By analysing the measurement-disturbance required
in models of these phenomena, we find that the strong measurement version of
logical pre- and post-selection paradoxes actually constitute a direct
manifestation of quantum contextuality. The proof hinges on under-appreciated
features of the paradoxes. In particular, we show by example that it is not
possible to prove contextuality without Luders-von Neumann updates for the
intermediate measurements, nonorthogonal pre- and post-selection, and 0/1
probabilities for the intermediate measurements. Since one of us has recently
shown that anomalous weak values are also a direct manifestation of
contextuality [arXiv:1409.1535], we now know that this is true for both
realizations of logical pre- and post-selection paradoxes.
