  There are two different and logically independent concepts of
noncontextuality in quantum mechanics. First, an ontological (hidden variable)
model for quantum mechanics is called noncontextual if every ontic (hidden)
state determines the probability of the outcomes of every measurement
independently of what other measurements are simultaneously performed. Second,
an ontological model is noncontextual if any two measurements which are
represented by the same self-adjoint operator or, equivalently, which have the
same probability distribution of outcomes in every quantum state also have the
same probability distribution of outcomes in every ontic state. I will call the
first concept simultaneous noncontextuality, the second measurement
noncontextuality. In the paper I will overview and critically analyze some of
the most significant accounts of contextuality in the literature and subsume
them under these two categories.
