Quantum logic as a fragment of independence-friendly logic

Journal of Philosophical Logic 31 (3):197-209 (2002)
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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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Citations of this work

Generalized quantifiers.Dag Westerståhl - 2008 - Stanford Encyclopedia of Philosophy.
Independence-friendly logic and axiomatic set theory.Jaakko Hintikka - 2004 - Annals of Pure and Applied Logic 126 (1-3):313-333.
Independence friendly logic.Tero Tulenheimo - 2010 - Stanford Encyclopedia of Philosophy.
Negation in logic and in natural language.Jaakko Hintikka - 2002 - Linguistics and Philosophy 25 (5-6):585-600.

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References found in this work

The structure and interpretation of quantum mechanics.R. I. G. Hughes - 1989 - Cambridge: Harvard University Press.
The Principles of Mathematics Revisited.Jaakko Hintikka - 1996 - New York: Cambridge University Press.
Is Logic Empirical?Hilary Putnam - 1968 - Boston Studies in the Philosophy of Science 5.
Interpreting the Quantum World.Jeffrey Bub - 1998 - British Journal for the Philosophy of Science 49 (4):637-641.

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