Quantum logic as a fragment of independence-friendly logic
The author presents his hypothesis that noncommuting variables are irreducibly interdependent in the logic connected with the foundations of quantum mechanics. The logic of such dependence relations is presented as independence-friendly logic, previously introduced by the author, which uses a sentence-initial contradictory negation over and above the dual (strong) negation \(\sim\). In the case of a Hilbert space quantum logic, the latter one turns out to be orthocomplementation. The author shows that quantum logic can be interpreted also in frames of Boolean structures to which the additional operator \(\sim\) has been added.
scientific article; zbMATH DE number 1784294