Abstract
The working assumption of this paper is that noncommuting variables are irreducibly interdependent. The logic of such dependence relations is the author's independence-friendly (IF) logic, extended by adding to it sentence-initial contradictory negation ¬ over and above the dual (strong) negation ∼. Then in a Hilbert space ∼ turns out to express orthocomplementation. This can be extended to any logical space, which makes it possible to define the dimension of a logical space. The received Birkhoff and von Neumann “quantum logic” can be interpreted by taking their “disjunction” to be ¬(∼A & ∼B). Their logic can thus be mapped into a Boolean structure to which an additional operator ∼ has been added.
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Hintikka, J. Quantum Logic as a Fragment of Independence-Friendly Logic. Journal of Philosophical Logic 31, 197–209 (2002). https://doi.org/10.1023/A:1015742824326
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DOI: https://doi.org/10.1023/A:1015742824326