Contextuality in quantum mechanics is one of the main features that set it aside from "classical" theories. Before making such an assumption one wants to be convinced that a non-contextual model would not be able to replicate the same results.

Pre- and Post- Selection Paradoxes (PPS Paradoxes) are a good candidate to prove contextuality.

In 2014 it was proven that the existence of anomalous weak values in quantum mechanics makes it incompatible with any non-contextual model.

A year after that it was proven that a non-contextual model would not be able to replicate "Logical" PPS Paradoxes.

We try to relax the assumption that our PPS Paradoxes need to be logical by exploring the relationship between weak values and PPS paradoxes.

We show that we can relax the assumption for binary measurements and establish a methodology to generalize the result to an arbitrary number of possible outcomes.