Quantum Logic as a Fragment of Independence-Friendly Logic
- Jaakko Hintikka
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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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- Quantum Logic as a Fragment of Independence-Friendly Logic
Journal of Philosophical Logic
Volume 31, Issue 3 , pp 197-209
- Cover Date
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- Online ISSN
- Kluwer Academic Publishers
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- quantum logic
- independence-friendly logic
- Boolean structures
- Jaakko Hintikka (1)
- Author Affiliations
- 1. Department of Philosophy, Boston University, USA