  I will argue that the Peres-Mermin square does not necessarily rule out a
value-definite (deterministic) noncontextual hidden variable model if the
operators are not given a physical interpretation satisfying the following two
requirements: (i) each operator is uniquely realized by a single physical
measurement; (ii) commuting operators are realized by simultaneous
measurements. To underpin this claim, I will construct three hidden variable
models for three different physical realizations of the Peres-Mermin square:
one violating (i), another violating (ii), and a third one violating both (i)
and (ii).
