of modes and the observations of the results: $(ZZ,\pm1,\pm1)$, $(ZX,\pm1,\pm1)$, $(XZ,\pm1,\pm1)$ and $(XX,\pm1,\pm1)$.

In the sense of the observation space, all 16 outcomes are observable. For example, consider the case $ZZ$ where both modes are 1. By , the conditional probabilities ${\mathcal P}\big[(+1,+1){\:\vert\:}ZZ\big]$, ${\mathcal P}\big[(+1,-1){\:\vert\:}ZZ\big]$, ${\mathcal P}\big[(-1,+1){\:\vert\:}ZZ\big]$ are $1/3$. Accordingly $${\mathcal P}\big[\{(+1,+1),(+1,-1),(-1,+)\}{\:\vert\:}ZZ\big] = 1$$ and so ${\mathcal P}\big[(-1,-1){\:\vert\:}ZZ\big] = 0$. Thus, in the case $ZZ$, it is impossible to have $-1$ on the left and on the right in the same trial. But, like event $\emptyset$, the event $\{(ZZ,-1,-1)\}$ is observable in the sense of §\[sec:frame\].

Thus ${\mathcal P}$ is defined on all events. The extension problem is trivial in Hardy’s case, and negative probabilities do not arise.

The presence of contextuality and the absence of negativity seem to contradict Robert Spekkens’s claim that negativity and contextuality are equivalent forms of nonclassicality [@Spekkens]. Earlier, in a lengthy footnote in Section 6 of [@G236], we showed that the equivalence claim is unsubstantiated.

Limitation
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The notion of observation spaces was motivated by quantum mechanics with its observables, i.e., Hermitian operators, which may or may not be coobservable, i.e., commeasurable. Unfortunately, as this section shows, this notion is too simplistic to faithfuly 