The Metalogic of Quantum Logic

Abstract
The logic of quantum physical propositions can be established by means of dialogs which take account of the general incommensurability of these propositions. Investigated first are meta-propositions which state the formal truth of object-propositions. It turns out that the logic of these meta-propositions is equivalent to ordinary logic. A special class of meta-propositions which state the material truth of object-propositions may be considered as quantum logical modalities. It is found that the logic of these modalities contains all the quantum logical restrictions and thus differs essentially from the modal calculi of ordinary logic.
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