{E}_{S}\cup \mathcal{E}_{S}^{\bot }$, the sentence $E(x)$ obviously is certainly true, hence true (certainly false, hence false) iff $E\in \mathcal{E}_{S}$ ($E\in \mathcal{E}_{S}^{\bot }$). On the contrary, no prediction of the truth value of $E(x)$ can be done if $E\notin \mathcal{E}_{S}\cup \mathcal{E}_{S}^{\bot }$. Thus, the difference between the standard and the SR interpretation reduces to the fact that, whenever $E\in \mathcal{E}_{S}^{I}$, $E(x)$ is meaningless within the former, while it has a truth value that cannot be predicted by QM within the latter.

Empirical proof in QM
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The results at the end of Secs. 2.4 and 2.5 show that, whenever $x$ is in the state $S$, the truth value of the sentence $E(x)$ can be predicted (or *theoretically proved*) iff $E\in \mathcal{E}_{S}\cup \mathcal{E}_{S}^{\bot }$, both in the standard and in the SR interpretation. One is thus led to wonder whether and when the truth value of $E(x)$ can be determined empirically. At first glance, it seems sufficient to test $x$ by means of a registering device belonging to $E$ (Sec. 2.1). This is untrue according to the standard as well as the SR interpretation. Indeed, both interpretations maintain that a single test modifies, whenever $E\notin 
\mathcal{E}_{S}\cup \mathcal{E}_{S}^{\bot }$, the state $S$ of the physical object $x$, so that its result refers to the final state after the test, which is different from $S$ (moreover, within the standard interpretation, $E(x)$ has no truth value whenever $E\notin \mathcal{E}_{S}\cup \mathcal{E}_{S}^{\bot }$). Thus, a test of $E(x)$ is physically meaningful iff $E\in 
\mathcal{E}_{S}\cup \mathcal{E}_{S}^{\bot }$, since only in this case it does not modify the state $S$. It follows that an *empirical proof* of the truth value of $E(x)$ can be given iff a theoretical proof of this value exists, and it consists in checking whether $E\in \mathcal{E}_{S}$ or $E\in \mathcal{E}_{S}^{\bot }$. Then, the characterizations of $\mathcal{E}_{S}$ and $\mathcal{E}_{S}^{\bot }$ in Se