Journal of Philosophical Logic

, Volume 31, Issue 3, pp 197-209

First online:

Quantum Logic as a Fragment of Independence-Friendly Logic

  • Jaakko HintikkaAffiliated withDepartment of Philosophy, Boston University

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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.

quantum logic independence-friendly logic negation Boolean structures