 certainly true or certainly false, respectively, according to the SR interpretation with its Tarskian concept of truth. The remaining statements are meaningless according to the former interpretation, while they have truth values according to the latter: these values, however, may change when different objects in the same state are considered, and cannot be predicted in QM (which is, in this sense, an incomplete theory).

Because of its intuitive, philosophical and technical advantages, we adopt the SR interpretation in the present paper. It is then important to observe that our definitions and reasonings take into account only statements that are certainly true (certainly false) in the sense explained above, hence they actually do not depend on the choice of the interpretation of QM (standard or SR). Thus, our reinterpretation of QL should be acceptable also for logicians and physicists who do not agree with our epistemological position. Of course, if the SR interpretation is not accepted one loses all philosophical advantages of the integrated perspective mentioned at the beginning of this section.

Let us come now to empirical justification. Whenever a statement $E(x)$ is certainly true (certainly false), its truth (falsity) can be predicted within QM if the property $E$ and the state $S$ of $x$ are known, and can be checked (by means of nontrivial physical procedures, see Sec. 2.6). Hence, we can say that the assertion of $E(x)$ ($E^{\bot }(x)$) is empirically justified, since we can both deduce the truth of $E(x)$ ($E^{\bot }(x)$) inside QM and provide an empirical proof of it. More formally, one can introduce an assertion sign $\vdash $ and say that $E(x)$ is certainly true (certainly false) iff $\vdash E(x)$ ($\vdash E^{\bot }(x)$) is empirically justified. In this way a semantic notion (certainty of truth) is translated into a pragmatic notion (empirical justification). Now, we remind that a pragmatic extension of a classical language and some general properties of the concept of justification have been 