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Quantum Logic as a Fragment of Independence-Friendly Logic

Jaakko Hintikka
Journal of Philosophical Logic
Vol. 31, No. 3 (Jun., 2002), pp. 197-209
Published by: Springer
Stable URL: http://www.jstor.org/stable/30226931
Page Count: 13
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Quantum Logic as a Fragment of Independence-Friendly Logic
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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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