Quantum logic as a fragment of independence-friendly logic

Journal of Philosophical Logic 31 (3):197-209 (2002)
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
Keywords quantum logic  independence-friendly logic  negation  Boolean structures
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Jaakko Hintikka (2004). Independence-Friendly Logic and Axiomatic Set Theory. Annals of Pure and Applied Logic 126 (1-3):313-333.
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